Category People from Harpenden ar de HaroldScottMacDonaldCoxeter es HaroldScottMacDonaldCoxeter eu HaroldScottMacDonaldCoxeter fr HaroldScottMacDonaldCoxeter it HaroldCoxeter he ht HaroldScottMacDonaldCoxeter nl HaroldCoxeter ja nn HaroldScottMacDonaldCoxeter pl HaroldScottMacDonaldCoxeter pt HaroldScottMacDonaldCoxeter sv H.S.M. Coxeter zh ... spouse Hendrina, died in 1999 children Susan Thomas, and a son, Edgar HaroldScottMacDonald Donald Coxeter , Post nominals country CAN CC February 9, 1907 &ndash March 31, 2003 ref cite doi 10.1098 rsbm.2006.0004 ref was a British born Canadian geometer. Coxeter is regarded as one of the great ...Infobox scientist name H. S. M. Donald Coxeter image Coxeter.jpg image size 240px caption birth date ... In his youth, Coxeter composed music and was an accomplished pianist at the age of 10. ref name Roberts Roberts, Siobhan, King of Infinite Space Donald Coxeter, The Man Who Saved Geometry , Walker ... and more via algebra. Coxeter went up to Trinity College, Cambridge Trinity College , University ..., and his doctorate in 1931. ref name Roberts ref name MacTutor MacTutor Biography id Coxeter ref In 1932 ... he spent a further year at Princeton as a Procter Fellow. ref name MacTutor In 1936 Coxeter moved ... of Buckminster Fuller . Coxeter, M. S. Longuet Higgins and J. C. P. Miller were the first ... have awarded the Coxeter James Prize in his honor. In 1990, he became a Foreign Member of the American ... 3762 accessdate 26 May 2010 ref Works Coxeter, Longuet Higgins, Miller, Uniform polyhedra , Philosophical ... , Cambridge University Press H.S.M. Coxeter, R. Frucht and D. L. Powers, Zero Symmetric Graphs , 1981 ... Writings of H.S.M. Coxeter. John Wiley, 1995, ISBN 0 471 01003 0 cite book author Coxeter, H ... first Chandler editor1 link Chandler Davis editor2 last Ellers editor2 first Erich W title The Coxeter ... more details
ScottMacDonald may refer to ScottMacDonald musician , member the Canadian band Spoons ScottMacDonald actor , American actor Scott McDonald , Australian footballer hndis Macdonald, Scott ... more details
HaroldScott may refer to Harold Richard Scott 1887 1969 , Commissioner of the London Metropolitan Police from 1945 to 1953 Harold Russell Scott, Jr. 1935 2006 American stage director and actor Harold Scotty Scott , American vocalist with The Temprees trio HaroldScott actor , British actor See also Harry Scott disambiguation hndis Scott, Harold ... more details
Sir HaroldMacdonald Steward 8 September 1904 &ndash 3 March 1977 was a United Kingdom British consulting engineer and Conservative Party UK Conservative Party politician. He was the Member of Parliament MP for Stockport South UK Parliament constituency Stockport South for nine years, and later became Leader of Liverpool City Council . Engineering training Steward was born in Rainhill , near St Helens, Merseyside St Helens . He went to the local secondary school and to Cowley School in St Helens. He went into business at the age of 14, continuing to train in engineering at the St Helens Municipal Technical College. Steward later became a production engineering manager, and later still a development engineer he worked for the same company all through. During the Second World War he was seconded to work on radar research, and after the end of the war, served on an inter services mission to former enemy countries. Involvement in politics Already interested in politics he had won a Conservative Party prize for public speaking before the war , Steward was appointed a Justice of the Peace for Lancashire in 1951 and fought Liverpool Edge Hill UK Parliament constituency Liverpool Edge Hill at the United Kingdom general election, 1951 general election later that year . This was a near marginal constituency, although in the result, Labour improved its majority in the constituency against the national trend. Steward was elected to Liverpool City Council in 1953. Byelection candidate In January 1955, Steward was selected from 60 applicants to be Conservative candidate for Stockport South UK Parliament constituency Stockport South where a byelection was pending after Sir Arnold Gridley, 1st Baron Gridley Arnold Gridley was given a peerage. In a straight fight with a Labour candidate ... Steward, Harold ALTERNATIVE NAMES SHORT DESCRIPTION British politician DATE OF BIRTH 8 September 1904 PLACE OF BIRTH DATE OF DEATH 3 March 1977 PLACE OF DEATH DEFAULTSORT Steward, Harold Category 1904 ... more details
Notability Astro date February 2012 Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Coxeter symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered March 7, 1997 designations yes mp name 18560 alt names 1997 EO7 named after Harold Scott MacDonald Coxeter mp category orbit ref epoch May 14, 2008 aphelion 3.7193981 perihelion 2.5918555 semimajor eccentricity 0.1786559 period 2047.5140421 avg speed inclination 9.27665 asc node 329.18394 mean anomaly 227.06899 arg peri 324.99191 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 12.9 18560 Coxeter 1997 EO7 is a Asteroid belt main belt asteroid discovered on March 7, 1997 by P. G. Comba at Prescott Observatory Prescott . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 18560 Coxeter JPL Small Body Database Browser on 18560 Coxeter MinorPlanets Navigator 18559 1997 EN2 18561 1997 EY34 MinorPlanets Footer DEFAULTSORT Coxeter Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Paul G. Comba Category Astronomical objects discovered in 1997 beltasteroid stub fa it 18560 Coxeter pl 18560 Coxeter pt 18560 Coxeter uk 18560 vi 18560 Coxeter yo 18560 Coxeter ... more details
Infobox person name ScottMacDonald image image caption Macdonald in Star Trek birth date 1959 age 52 53 nationality United States American occupation Actor years active 1993 present ScottMacDonald born 1959 is an United States American actor . He is best known for his recurring roles as Captain Manning on short lived series Threshold TV series Threshold , Burley from HBO series Carniv le , and as List of minor recurring characters in Star Trek Enterprise Dolim Commander Dolim from Star Trek Enterprise , and as the title character from 1996 horror film Jack Frost 1996 film Jack Frost . He grew up in Libby, Montana and graduated from Washington State University and received an Master of Fine Arts MFA in acting theatre from the California Institute of the Arts . He has also done stage theatre stage acting, including on Broadway theatre Broadway . Films Fire in the Sky 1993 ... as Dan Walton A Rats Tale 1996 ... as Rudi Rake Rat voice Jack Frost 1996 film Jack Frost 1996 ... as Jack Frost Character voice William Psychspeare s The Taming of the Shrink 1998 ... as Bulbis The Rat Pack film The Rat Pack 1998 ... as Tourist Babylon 5 A Call to Arms 1999 ... as First officer Bad City Blues 1999 ... as Mack Seven Girlfriends 1999 ... as Scot, the Jogger Jack Frost 2 Revenge of the Mutant Killer Snowman 2000 ... as Jack Frost voice Straight Into Darkness 2004 ... as Deming Jarhead film Jarhead ... of Tara 2 episodes Video Games L.A. Noire External links imdb name 531924 ScottMacDonald memoryalpha ScottMacDonald http www.webcitation.org query?url http www.geocities.com actorzinc Scott MacDonald.html&date 2009 10 25 12 01 44 ScottMacDonald at Actorz Inc. Persondata Metadata see Wikipedia Persondata . NAME Macdonald, Scott ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1959 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Macdonald, Scott Category 1959 births Category American ... Actors from Montana fr ScottMacDonald ... more details
distinguish Longest element of a Coxeter group In mathematics , the Coxeter number h is the order group theory order of a Coxeter element of an irreducible Coxeter group , hence also of a root system or its Weyl group . It is named after H.S.M. Coxeter . ref Citation title The Coxeter Legacy Reflections and Projections last Coxeter first HaroldScottMacdonald authorlink coauthors Chandler Davis, Erlich ... http books.google.com ?id cKpBGcqpspIC&pg PA107&dq 22Coxeter number 22 22Donald Coxeter 22 postscript none ref Definitions Warning this article assumes a finite Coxeter group. For infinite Coxeter groups, there are multiple conjugacy classes of Coxeter elements, and they have infinite order. There are many different ways to define the Coxeter number h of an irreducible root system. A Coxeter element ... . The Coxeter number is the number of roots divided by the rank. The Coxeter number is the order of a Coxeter ... sub sub i sub for simple roots sub i sub , then the Coxeter number is 1 m sub i sub The dimension of the corresponding Lie algebra is n h 1 , where n is the rank and h is the Coxeter number. The Coxeter number is the highest degree of a fundamental invariant of the Weyl group acting on polynomials. The Coxeter number is given by the following table class wikitable style text align center margin 1em auto colspan 2 Coxeter group Coxeter number h Dual Coxeter number Degrees ..., p The invariants of the Coxeter group acting on polynomials form a polynomial algebra whose generators ... of a Coxeter element are the numbers e sup 2 i m &minus 1 h sup as m runs through the degrees ... is important in the Coxeter plane Coxeter plane , below. Coxeter elements Expand section date December 2008 Coxeter elements of math A n 1 cong S n math , considered as the symmetric group on n elements, are n cycles for simple reflections the adjacent transpositions math 1,2 , 2,3 , dots math , a Coxeter ... is a rotation by math 2 pi m math . Coxeter plane File E8Petrie.svg thumb Projection of E sub 8 sub ... more details
Other people2 HaroldScott disambiguation HaroldScott Infobox person name HaroldScott image RIVERSIDE SHAKESPEARE COMPANY HAROLDSCOTT as BRUTUS.jpg caption Scott as Brutus in the Riverside Shakespeare ... Morristown, New Jersey death date 16 July 2006 death place Newark, New Jersey Harold Russell Scott ... Robertson title HaroldScott, 70, Director Who Broke Racial Barriers, Dies url http query.nytimes.com ... Bot retrieved archive archivedate 2008 05 14 ref Life and career Scott was born in Morristown, New Jersey . His mother was a housewife and his father, Harold Russell Scott, Sr., was a general ... earned such in a major regional theatre. References reflist External links IBDB name 16106 Harold Russell Scott, Jr. IMDb name 779212 HaroldScott Persondata Metadata see Wikipedia Persondata . NAME Scott, Harold Russell, Jr. ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 6 September 1935 PLACE ... Scott, Harold Russell, Jr. Category 1935 births Category 2006 deaths Category African American ... August 2006 accessdate 2008 06 02 ref Scott first became known for his work as an electrifying stage ... djvu.txt ref Scott was educated at Philips Exeter Academy and Harvard. He had a career as a stage director ... of the Obie Award for acting in Jean Genet s Deathwatch in 1959, Scott also played on Broadway in The Cool World. Scott was chosen by Elia Kazan to be an original member of the Repertory Theatre of Lincoln ..., Scott returned to Off Broadway to play Brutus in a modern dress production of Shakespeare s Caesar ... date 14 March 1984 accessdate ref Scott staged numerous innovative productions in New York and at regional ... in Paul Robeson on Broadway twice in 1988 and again in 1995. Scott also directed the twenty fifth ..., DC. Scott s production received nine National Theater Awards from the NAACP, including best director ... School of the Arts date accessdate 2008 06 02 ref Scott was head of the directing program at the Mason ... 88, and Acting Artistic Director, 1989 90. In February 2006, Scott directed his final play, Yellowman ... more details
Other people2 HaroldScott disambiguation unreferenced date November 2010 Sir Harold Richard Scott , Royal Victorian Order GCVO , Order of the Bath KCB , Order of the British Empire KBE 1887 1969 was Commissioner of Police of the Metropolis Commissioner of the Metropolitan Police Service Metropolitan Police from 1945 to 1953. Scott was born in Dublin , England and raised in Bruton , Somerset . He was educated at Sexey s School and later Jesus College, Cambridge Jesus College of the University of Cambridge . In 1911, he joined the Home Office as a civil servant , where he worked in various capacities including Secretary to the Labour Resettlement Committee 1918 1919 and Chairman of the Prison Commission England and Wales Prison Commission 1932 1939 . With the outbreak of World War II , Scott s work took on a more military capacity, as he joined London s Civil Defence Administration until he was appointed as Permanent Secretary of the Ministry of Aircraft Production in 1943. In late 1944, the Home Secretary Herbert Morrison asked Scott to accept the post as Metropolitan Police Commissioner when the war was over. The appointment in 1945 caused a stir in police circles Scott was the first Commissioner without a police or military background since Sir Richard Mayne who had been a lawyer when appointed . Unlike all subsequent commissioners, he was not a career police officer. Scott s administration ... Sir John Nott Bower years 1945 1953 s end Persondata Metadata see Wikipedia Persondata . NAME Scott, Harold ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1887 PLACE OF BIRTH DATE OF DEATH 1969 PLACE OF DEATH DEFAULTSORT Scott, Harold Category 1887 births Category 1969 deaths Category Alumni .... Scott presided over several high profile cases during his time with the Met, including the Derek Bentley trial for the murder of police officer PC Sidney Miles. In 1951, Scott introduced a British Police Cadets police cadet training scheme for young people aged between 16 and 18. Scott retired ... more details
In mathematics , a Coxeter group , named after HaroldScottMacDonaldCoxeter H.S.M. Coxeter , is an group ... symmetries. Indeed, the finite Coxeter groups are precisely the finite reflection group Euclidean ..., not all Coxeter groups are finite, and not all can be described in terms of symmetries and Euclidean reflections. Coxeter groups were introduced Harv Coxeter 1934 as abstractions of reflection group s, and finite Coxeter groups were classified in Harv Coxeter 1935 . Coxeter groups find applications in many areas of mathematics. Examples of finite Coxeter groups include the symmetry group s of regular polytope s, and the Weyl group s of simple Lie algebra s. Examples of infinite Coxeter groups ... and Harv Davis 2007 . Definition Formally, a Coxeter group can be defined as a group mathematics .... The pair W,S where W is a Coxeter group with generators S r sub 1 sub ,..., r sub n sub is called Coxeter system . Note that in general S is not uniquely determined by W . For example, the Coxeter groups of type BC sub 3 sub and A sub 1 sub x A sub 3 sub are isomorphic but the Coxeter systems are not equivalent ... yx m yy 1 yx m math . Coxeter matrix The Coxeter matrix is the n × n , symmetric matrix with entries ... such that all nondiagonal entries are greater than 1 serves to define a Coxeter group. The Coxeter matrix can be conveniently encoded by a Coxeter Dynkin diagram Coxeter diagram , as per ... if and only if they are not connected by an edge. Furthermore, if a Coxeter graph has two or more ... of Coxeter graphs yields a direct product of groups direct product of Coxeter groups. The Coxeter ... M sub i,j sub . The Cartan matrix is useful because its determinant determines whether the Coxeter ... Coxeter group A sub 1 sub A sub 1 sub A sub 2 sub math tilde I 1 math A sub 3 sub B sub 3 sub D sub 4 sub math tilde A 3 math align center Coxeter diagram CDD node 2 node CDD node 3 node CDD node ... nodes split2 node align center Coxeter matrix math left begin smallmatrix 1 & 2 2 & 1 end smallmatrix ... more details
Notes reflist References HaroldScottMacDonaldCoxeter H.S.M. Coxeter Kaleidoscopes Selected Writings ...In geometry , Coxeter notation is a system of classifying symmetry group s, describing the angles between with fundamental reflections of a Coxeter group . It uses a bracketed notation, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter , and has been more comprehensively ... For Coxeter group s defined by pure reflections, there is a direct correspondence between the bracket notation and Coxeter Dynkin diagram graphs. The numbers in the bracket notation represent the mirror reflection orders in the branches of the Coxeter graph. The Coxeter notation is simplified with exponents ... superscript values at the branch lengths. Coxeter groups formed by cyclic graphs are represented ... top class wikitable Finite Coxeter groups Rank Group BR symbol Coxeter notation Bracket notation Coxeter Dynkin diagram Coxeter graph align center 2 A sub 2 sub 3 CDD node 3 node align center 2 ... Affine Coxeter groups Group BR symbol Coxeter notation Bracket notation Coxeter Dynkin diagram Coxeter ... 3a nodea 3a nodea 3a nodea 3a nodea class wikitable Compact Hyperbolic Coxeter groups Group BR symbol Coxeter notation Bracket notation Coxeter Dynkin diagram Coxeter graph align center p,q BR with 2 ... a node to a finite group s graph. The Coxeter graph usually leaves order 2 branches undrawn, but the bracket notation includes an explicit 2 to connect the subgraphs. So the Coxeter graph, CDD node ... Coxeter groups are categorized by their rank, being the number of nodes in its Coxeter Dynkin diagram Coxeter graph . The structure of the groups are also given with their abstract group types ... Order group theory order 2. It is represented as a Coxeter Dynkin diagram Coxeter graph with a single ... are ignored, leaving the identity group in this simplest case. class wikitable Group Coxeter notation CoxeterCoxeter Dynkin diagram Coxeter diagram Order Description align center C sub 1 sub ... more details
otheruses4 the 3 regular graph the graph associated with a Coxeter group Coxeter diagram infobox graph name Coxeter graph image Image Coxeter graph.svg 250px image caption The Coxeter graph namesake vertices ... graph Hypohamiltonian In the mathematics mathematical field of graph theory , the Coxeter ... Coxeter Graph ref All the cubic graph cubic distance regular graph s are known. ref Brouwer, A. E. Cohen, A. M. and Neumaier, A. Distance Regular Graphs. New York Springer Verlag, 1989. ref The Coxeter graph is one of the 13 such graphs. Properties The Coxeter graph has chromatic number 3, chromatic ... vertex connected graph and a 3 k edge connected graph edge connected graph . The Coxeter graph is hypohamiltonian ..., but an 11 crossing, 26 vertex graph may exist OEIS id A110507 . The Coxeter graph may be constructed ... title From the Coxeter graph to the Klein graph journal Journal of Graph Theory year 2011 doi 10.1002 jgt.20597 arxiv 1002.1960 . ref Algebraic properties The automorphism group of the Coxeter graph ... ref It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Coxeter ... edge to any other edge. According to the Foster census , the Coxeter graph, referenced as F28A ... Graphs Up to 768 Vertices. J. Combin. Math. Combin. Comput. 40, 41 63, 2002. ref The Coxeter graph ... graph that contains no Hamiltonian cycle , the Coxeter graph is a counterexample to a variant of the Lov sz ... by the Coxeter graph. Only five examples of vertex transitive graph with no Hamiltonian cycles are known the complete graph K sub 2 sub , the Petersen graph , the Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing each vertex with a triangle. ref Royle ... . ref The characteristic polynomial of the Coxeter graph is math x 3 x 2 8 x 1 7 x 2 2 x 1 6 math . It is the only .... Gallery gallery Image Edge excised Coxeter graph.svg The graph obtained by any edge excision from the Coxeter is Hamilton connected. Image coxeter graph 3COL.svg The chromatic number of the Coxeter ... more details
In mathematics, the Coxeter complex , named after H. S. M. Coxeter , is a geometrical structure a simplicial complex associated to a Coxeter group . Coxeter complexes are the basic objects that allow the construction of building mathematics buildings they form the apartments of a building. Construction The canonical linear representation The first ingredient in the construction of the Coxeter complex associated to a Coxeter group W is a certain representation mathematics representation of W , called the canonical representation of W . Let math W,S math be a Coxeter group Coxeter system associated to W , with Coxeter group Coxeter matrix Coxeter matrix math M m s,t s,t in S math . The canonical representation is given by a vector space V with basis of formal symbols math e s s in S math , which is equipped with the symmetric bilinear form math B e s,e t cos left frac pi m s,t right math . The action of W on this vector space V is then given by math s v v 2 frac B e s,v B e s,e s e s math ... foundational properties in the theory of Coxeter groups for instance, the bilinear form B is positive ... chamber math mathcal C math . The Coxeter complex Once one has defined the Tits cone X , the Coxeter ... n are Coxeter groups, of corresponding type math mathrm I 2 n math . These have the presentation math ... 3, we get the Coxeter group of type math mathrm I 2 3 mathrm A 2 math , acting on an equilateral ... chambers, as seen below File Spherical dihedral complex.svg 300px The Coxeter complex is then the corresponding ... and math x 1 math . This group has the Coxeter presentation math left langle s, t , left , s 2, t 2 ... at the integers. This is the Coxeter complex of the infinite dihedral group. Alternative construction of the Coxeter complex Another description of the Coxeter complex uses standard cosets of the Coxeter ... math for some subset J of S . For instance, math W S W math and math W emptyset 1 math . The Coxeter ..., Theory and Applications . Springer, 2008. Category Group theory Category Coxeter groups Category ... more details
Thomas Coxeter 1689 1747 was an English literary antiquary. Life Born at Lechlade in Gloucestershire on 20 September 1689, he was educated at Coxwell , Berkshire , and at Magdalen School in Oxford . On 7 July 1705 he was entered a commoner of Trinity College, Oxford . Having completed his course, he came to London to practise the Civil law legal system civil law but in 1710, on the death of his patron, Sir John Cook , dean of arches , he abandoned the legal profession and devoted himself to literary and antiquarian pursuits. In 1747 he was appointed secretary to a society for the encouragement of an essay towards a complete English history. He died of a fever on 19 April 1747, and was buried in the chapel yard of the Royal Hospital of Bridewell . His daughter was supported by Samuel Johnson she died in 1807. Works An elegy in a book entitled Astr a Lacrimans , published anonymously in 1710, was probably written by Coxeter. In 1720 he contributed one or more of the indexes to John Hudson classicist John Hudson s edition of Flavius Josephus Josephus and in 1739 he published a new edition of the Life of Bishop Fisher often attributed to Richard Hall canon of St Omer Richard Hall , its translator into Latin. ref http www.joh.cam.ac.uk library special collections manuscripts post medieval pmml22 ref ref ODNBweb id 11979 title Hall, Richard first John J. last LaRocca ref Coxeter was a collector of old English plays, and allowed the Shakespearean editor, Lewis Theobald Theobald , to make ... Buckhurst . Coxeter s manuscript collections were largely used in Theophilus Cibber s Lives of the Poets ... s works appeared, collated by Mr. Coxeter it was criticised by William Gifford . Others the Edinburgh ... Coxeter, Thomas first Graham last Parry ref References Dictionary of National Biography , Coxeter ... Persondata Metadata see Wikipedia Persondata . NAME Coxeter, Thomas ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1689 PLACE OF BIRTH DATE OF DEATH 1747 PLACE OF DEATH DEFAULTSORT Coxeter, Thomas ... more details
File Coxeter helix.png thumb Coxeter regular tetrahedral helix File Boerdijk helical sphere packing.png thumb A Boerdijk helical sphere packing has each sphere centered at a Vertex geometry vertex of the Coxeter helix. Each sphere is in contact with 6 neighboring spheres. The Boerdijk Coxeter helix , named after H. S. M. Coxeter and A. H. Boerdijk , is a linear stacking of regular tetrahedron tetrahedra . There are two Chirality mathematics chiral forms, with either clockwise or counterclockwise windings. Contrary to any other stacking of Platonic solids , the Boerdijk Coxeter helix is not rotationally repetitive. Even in an infinite string of stacked tetrahedra, no two tetrahedra will have the same orientation. Buckminster Fuller named it a tetrahelix and considered them with regular and irregular tetrahedral elements. ref http www.rwgrayprojects.com synergetics s09 p3000.html ref See also Toroidal polyhedron Notes reflist References H.S.M. Coxeter , Regular Complex Polytopes , Cambridge University, 1974. A.H. Boerdijk, Philips Res. Rep. 7 1952 30 The c brass structure and the Boerdijk Coxeter helix , E.A. Lord, S. Ranganathan, 2004, pp. 123 125 http materials.iisc.ernet.in lord webfiles icq8.pdf Eric A. Lord, Alan Lindsay Mackay, Srinivasa Ranganathan, New geometries for new materials , p 64, sec 4.5 The Boerdijk Coxeter helix J.F. Sadoc and N. Rivier, Boerdijk Coxeter helix and biological helices The European Physical Journal B Condensed Matter and Complex Systems, Volume 12, Number 2, 309 318, DOI 10.1007 s100510051009 http epjb.edpsciences.org index.php?option com article&access standard&Itemid 129&url articles epjb abs 1999 22 b8774 b8774.html External links http flickriver.com photos fdecomite 5403437189 Boerdijk Coxeter helix animation Category Polyhedra polyhedron stub ... more details
infobox graph name Tutte Coxeter graph image Image Tutte eight cage.svg 180px image caption namesake W. T. Tutte br H. S. M. Coxeter vertices 30 edges 45 automorphisms 1440 Aut S sub 6 sub girth 8 chromatic ... Distance transitive In the mathematics mathematical field of graph theory , the Tutte Coxeter graph ... and H. S. M. Coxeter it was discovered by Tutte 1947 but its connection to geometric configurations was investigated by both authors in a pair of jointly published papers Tutte 1958 Coxeter 1958a . All ..., A. Distance Regular Graphs. New York Springer Verlag, 1989. ref The Tutte Coxeter is one of the 13 ... of the Tutte Coxeter graph is due to Coxeter 1958b , based on much earlier work by Sylvester 1844 ... Coxeter graph can be viewed as having one vertex per duad, one vertex per syntheme, and an edge connecting each syntheme to each of the three duads that form it. Based on this construction, Coxeter showed that the Tutte Coxeter graph is a symmetric graph it has a group mathematics group of 1440 ... of permutations on six elements Coxeter 1958b . The inner automorphism s of this group correspond to permuting ... on the Tutte Coxeter graph by permuting the vertices on each side of its bipartition while keeping ... swap one side of the bipartition for the other. As Coxeter showed, any path of up to five edges in the Tutte Coxeter graph is equivalent to any other such path by one such automorphism. Gallery gallery Image Tutte Coxeter graph crossing number.svg The Crossing number graph theory crossing number of the Tutte Coxeter graph is 13. Image Tutte Coxeter graph 2COL.svg The chromatic number of the Tutte Coxeter graph is 2. Image Tutte Coxeter graph 3color edge.svg The chromatic index of the Tutte Coxeter graph is 3. gallery References reflist cite journal author Coxeter, H. S. M. authorlink H. S. M. Coxeter title The chords of the non ruled quadric in PG 3,3 journal Canad. J. Math. volume 10 year 1958a pages 484 488 doi 10.4153 CJM 1958 047 0 cite journal author Coxeter, H. S. M. authorlink ... more details
distinguish Coxeter element of a Coxeter group In mathematics , the longest element of a Coxeter group is the unique element of maximal length function length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections. It is often denoted by w sub 0 sub . See Harv Humphreys 1992 loc Section 1.8 Simple transitivity and the longest element, http books.google.com books?id ODfjmOeNLMUC&pg PA15 pp. 15 16 and Harv Davis 2007 loc Section 4.6, pp. 51 53 . Properties A Coxeter group has a longest element if and only if it is finite only if is because the size of the group is bounded by the number of words of length less than or equal to the maximum. The longest element of a Coxeter group is the unique maximal element with respect to the Bruhat order . The longest element is an Involution mathematics involution has order 2 math w 0 1 w 0 math , by uniqueness of maximal length the inverse of an element has the same length as the element . ref name hum16 Harv Humphreys 1992 loc http books.google.com books?id ODfjmOeNLMUC&pg PA16 p. 16 ref For any math w in W, math the length satisfies math ell w 0w ell w 0 ell w . math ref name hum16 A reduced expression for the longest element is not in general unique. In a reduced expression for the longest element, every simple reflection must occur at least once. ref name hum16 If the Coxeter group is a finite Weyl group then the length of w sub 0 sub is the number of the positive root s. The open cell Bw sub ... 2 automorphism of the Coxeter diagram. ref Harv Davis 2007 loc Remark 13.1.8, p. 259 ref See also Coxeter element , a different distinguished element Coxeter number Length function References reflist refbegin citation title The Geometry and Topology of Coxeter Groups first Michael W. last Davis ... groups and Coxeter groups isbn 978 0 521 43613 7 first James E. last Humphreys year 1992 publisher Cambridge University Press refend Category Coxeter groups ... more details
In mathematics, the nil Coxeter algebra , introduced by harvtxt Fomin Stanley 1994 , is an algebra similar to the group algebra of a Coxeter group except that the generators are nilpotent . Definition The nil Coxeter algebra for the infinite symmetric group is the algebra generated by u sub 1 sub , u sub 2 sub , u sub 3 sub , ... with the relations u su b i p 2 0 u sub i sub u sub j sub u sub j sub u sub i sub if i &minus j 1 u sub i sub u sub j sub u sub i sub u sub j sub u sub i sub u sub j sub if i &minus j 1 These are just the relations for the infinite braid group , together with the relations u su b i p 2 0. Similarly one can define a nil Coxeter algebra for any Coxeter system , by adding the relations u su b i p 2 0 to the relations of the corresponding generalized braid group. References Citation last1 Fomin first1 Sergey last2 Stanley first2 Richard P. title Schubert polynomials and the nil Coxeter algebra doi 10.1006 aima.1994.1009 mr 1265793 year 1994 journal Advances in Mathematics issn 0001 8708 volume 103 issue 2 pages 196 207 Category Representation theory ... more details
The Coxeter James Prize is presented annually by the Canadian Mathematical Society . The award is presented to young mathematicians in recognition of outstanding contributions to mathematical research. The first award was presented in 1978. The prize was named in honor of the mathematicians Donald Coxeter and Ralph Duncan James Ralph James . ref http www.cms.math.ca Prizes info cj.html Coxeter James Prize ref Recipients of the Coxeter James Prize 2010 B lint Vir g 2009 Patrick Brosnan 2008 Ravi Vakil 2007 Vinayak Vatsal 2006 Jim Geelen 2005 Robert McCann 2004 Izabella Laba 2003 Jingyi Chen 2002 Lisa Jeffrey 2001 Kai Behrend 2000 Damien Roy 1999 Maciej Zworski 1998 Henri Darmon 1997 Michael Ward 1996 Nigel Higson 1995 Gordon Slade 1994 Mark Spivakovsky 1993 Jacques Hurtubise 1992 J.F. Jardine 1991 K. Murty 1990 Nassif Ghoussoub 1989 Alan Dow 1988 M. Ram Murty 1987 Jonathan Borwein 1986 Edwin A. Perkins 1985 Paul Selick 1984 Mark Goresky 1983 Man Duen Choi 1982 John Mallet Paret 1981 John James Millson 1980 Francis Clarke 1979 David W. Boyd 1978 Robert Moody References Reflist External links http www.cms.math.ca Canadian Mathematical Society Category Mathematics awards Category Awards established in 1978 Category Canadian science and engineering awards ... more details
In mathematics, the Coxeter Todd lattice K sub 12 sub , discovered by harvs txt yes author1 link H. S. M. Coxeter author2 link J. A. Todd last Coxeter last2 Todd year 1953 , is a the 12 dimensional even integral lattice group lattice of discriminant 3 sup 6 sup with no norm 2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 3, and is similar to the Barnes&ndash Wall lattice . The Coxeter&ndash Todd lattice can be made into a 6 dimensional lattice self dual over the Eisenstein integers. The automorphism group of this complex lattice has index 2 in the full automorphism group of the Coxeter&ndash Todd lattice and is a complex reflection group number 34 on the list with structure 6.PSU sub 4 sub F sub 3 sub .2, called the Mitchell group . The genus of the Coxeter&ndash Todd lattice was described by harv Scharlau Venkov 1995 and has 10 isometry classes, and all of them other than the Coxeter&ndash Todd lattice have a root system of maximal rank 12. The Coxeter&ndash Todd lattice is described in detail in harv Conway Sloane 1999 loc section 4.9 and harv Conway Sloane 1983 . References citation last Conway first J. H. last2 Sloane first2 N. J. A. title The Coxeter&ndash Todd lattice, the Mitchell group, and related sphere packings journal Math. Proc. Cambridge Philos. Soc. volume 93 year 1983 issue 3 pages 421 440 doi 10.1017 S0305004100060746 mr 0698347 Citation last1 Conway first1 John Horton author1 link John Horton Conway last2 Sloane first2 Neil J. A. author2 link Neil Sloane title Sphere Packings, Lattices and Groups publisher Springer Verlag location Berlin, New York edition 3rd series Grundlehren der Mathematischen Wissenschaften isbn 978 0 387 98585 5 year 1999 volume 290 mr 0920369 citation last Coxeter first H. S. M. last2 ... preprints 95 07.html title The genus of the Coxeter Todd lattice first Rudolf last Scharlau first2 ... K12.html Coxeter Todd lattice in Sloane s lattice catalogue Category Quadratic forms ... more details
In group theory , the Todd Coxeter algorithm , discovered by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation of a group G by generators and relations and a subgroup H of G , the algorithm enumerates the coset s of H on G and describes the permutation representation symmetric group permutation representation of G on the space of the cosets. If the order of a group G is relatively small and the subgroup H is known to be uncomplicated for example, a cyclic group , then the algorithm can be carried out by hand and gives a reasonable description of the group G . Using their algorithm, Coxeter and Todd showed that certain systems of relations between generators of known groups are complete, i.e. constitute systems of defining relations. The Todd Coxeter algorithm can be applied to infinite groups and is known to terminate in a finite number of steps, provided that the index group theory index of H in G is finite. On the other hand, for a general pair consisting of a group presentation and a subgroup, its running time is not bounded by any computable function of the index of the subgroup and the size of the input data. Description of the algorithm One implementation of the algorithm proceeds as follows. Suppose that math G langle X mid R rangle math , where math X math is a set of generating set of a group generators and math R math is a set of relation mathematics relations and denote by math X math the set of generators math X math and their inverses. Let math H langle h 1, h 2, ldots, h s rangle math where ... on the action of math G math on the cosets of math H math . See also Coxeter group References cite journal last Tood first J. A. last2 Coxeter first2 H. S. M. year 1936 title A practical method for enumerating ... cite book last Coxeter first W. O. J. last2 Moser year 1980 title Generators and Relations for Discrete ... de Todd Coxeter Algorithmus fr Algorithme de Todd Coxeter ru ... more details
see also Dynkin diagram Image Finite coxeter.png 325px right thumb Coxeter Dynkin diagrams for the fundamental finite Coxeter groups File Affine coxeter.PNG 325px right thumb Coxeter Dynkin diagrams for the fundamental affine Coxeter groups In geometry , a Coxeter Dynkin diagram or Coxeter diagram , Coxeter ... a Coxeter group , and Coxeter groups are classified by their associated diagrams. Dynkin diagram s are closely related objects, which differ from Coxeter diagrams in two respects firstly, branches labeled 4 or greater are directed graph directed , while Coxeter diagrams are undirected graph undirected ... Description Branches of a Coxeter Dynkin diagram are labeled with a rational number p , representing ..., so the corresponding branches are omitted. Geometric visualizations The Coxeter Dynkin diagram can ... Euclidean groups, and 2D spherical groups. For each the Coxeter diagram can be deduced by identifying ... 2 . class wikitable width 720 colspan 2 Image Coxeter dynkin plane groups.png 720px br Coxeter ... tilde G 2 math triangle. valign top Image Coxeter Dynkin 3 space groups.png 360px br Coxeter groups ... 3 math fills 1 24 of the cube. math tilde A 3 math fills 1 12 of the cube. Image Coxeter Dynkin sphere groups.png 360px br Coxeter groups in the sphere with equivalent diagrams. One fundamental domain ... with uniform polytopes Coxeter Dynkin diagrams can explicitly enumerate nearly all classes ... all but a few special cases have pure reflectional symmetry can be represented by a Coxeter Dynkin ... have their fundamental domain s represented by a set of n mirrors with a related Coxeter Dynkin diagram ... deleted. The resulting polytope will have a subsymmetry of the original Coxeter group . If all ... BC3 polytopes For example, the BC sub 3 sub Coxeter group has a diagram CDD node 4 node 3 node ... up Coxeter Dynkin diagram. The Wythoff symbol represents a special case of the Coxeter diagram for rank ... h01.svg 64px align center Coxeter BR diagram CDD node 1 4 node 3 node CDD node 1 4 node 1 3 node CDD ... more details
Wiktionary HaroldHarold may refer to TOC right People Given name Only include persons commonly know as simply HaroldHarold given name , including a list of persons and fictional characters with the name Harold Harefoot , or Harold I c. 1015 1040 , King of England from 1035 to 1040 Harold Godwinson , or Harold II c. 1022 1066 , the last Anglo Saxon king of England Harold martyr died 1168 , child martyr and saint Surname Harold surname , surname in the English language Fiction Childe Harold s Pilgrimage , a narrative poem by Lord Byron Harold film Harold film , a 2008 comedy Harold , an 1876 poem by Alfred, Lord Tennyson Harold and the Purple Crayon , a 1955 children s book by Crockett Johnson Harold and Maude , an American film Harold & Kumar , the common name for a series of stoner comedy films Harold, the Last of the Saxons , an 1848 book by Edward Bulwer Lytton, 1st Baron Lytton Other uses Harold, Ontario , Canada, a community in Stirling Rawdon township Harold horse , an American Thoroughbred racehorse Harold improvisation , an improvisational form popularized by Del Close and now performed by improvisational comedy groups worldwide Harold en Italie , the second symphony by Hector Berlioz Harold the Barrel , a song by Genesis from the album Nursery Cryme Harold or the Norman Conquest , an opera by Frederic Cowen Harold , an 1885 opera by Eduard N pravn k See also Harald disambiguation Herald disambiguation disambig Category Masculine given names de Harold es Harold fr Harold nl Harold ja no Harold pt Harold ru ... more details
Refimprove date June 2009 Notability date June 2009 Infobox Defunct Company fate Bankruptcy br Liquidation company name Harold s company logo company type company slogan foundation 1948 defunct 2008 location Dallas, Texas key people num employees 624 prior to bankruptcy filing industry Retail products Mens and Womens clothing revenue homepage Harold s Stores, Inc. was a Dallas, Texas Dallas based chain of traditional, high end classic styled ladies and men s specialty apparel stores. The chain operated 43 stores in 19 mid western and southeastern states in the United States . Prior to its bankruptcy filing, the company employed 624 people. The company was granted bankruptcy liquidation on November 10, 2008 and began liquidating its stores immediately. History Harold s was founded in 1948 in Norman, Oklahoma and was later moved to Dallas, Texas . The chain operated high end mens and women s clothing, usually located in upper class areas and shopping centers in the midwestern and southeastern parts of the United States. On November 10, 2008, the company was granted bankruptcy liquidation , claiming Increased competition and a weak economy have left us no choice but to cease operations. ref http www.foxbusiness.com story markets industries retail harolds going business sale going 992498596 Harold s Going Out Of Business Sale On Now ref References reflist External links http digital.library.okstate.edu encyclopedia entries H HA028.html Encyclopedia of Oklahoma History and Culture Harold s Category Companies based in Dallas, Texas Category Retail companies established in 1948 Category Companies disestablished in 2008 Category Article Feedback 5 Category 1948 establishments in the United States US retail company stub ... more details
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