In number theory , a perfectnumber is a positive integer that is equal to the sum of its proper positive ... aliquot sum . Equivalently, a perfectnumber is a number that is half the sum of all of its positive ... perfectnumber is 6 number 6 , because 1, 2 and 3 are its proper positive divisors, and 1 ... perfectnumber is 28 number 28 1 2 4 7 14. This is followed by the perfect numbers 496 number 496 and 8128 number 8128 OEIS id A000396 ... perfectnumber, with 33,550,336 being correctly identified for the first time. ref name Smith ... Even perfect numbers Euclid proved that 2 sup p 1 sup 2 sup p sup 1 is an even perfectnumber whenever ... s, after the seventeenth century monk Marin Mersenne , who studied number theory and perfect numbers ... even perfect numbers and Mersenne primes each Mersenne prime generates one even perfectnumber, and vice ... computing project. Because any even perfectnumber has the form 2 sup p 1 sup 2 sup p sup ... nowrap 2 sup p sup 1. Furthermore, any even perfectnumber except the first one is the nowrap ... mathworld.wolfram.com PerfectNumber.html PerfectNumber from MathWorld ref This can be reformulated as follows adding the digits of any even perfectnumber except 6 , then adding the digits of the resulting ... m . Owing to their form, 2 sup p 1 sup 2 sup p sup 1 , every even perfectnumber is represented ... perfect numbers exist. All perfect numbers are also Ore s harmonic number s, and it has been conjectured as well that there are no odd Ore s harmonic numbers other than 1. Any odd perfectnumber N must ... first DE title The second largest prime divisor of an odd perfectnumber exceeds ten thousand journal ... The third largest prime divisor of an odd perfectnumber exceeds one hundred journal Mathematics ... of any one such odd perfectnumber its escape, so to say, from the complex web of conditions ... perfect numbers have a very precise form odd perfect numbers either do not exist or are rare. There are a number ... more details
In mathematics , a multiply perfectnumber also called multiperfect number or pluperfect number is a generalization of a perfectnumber . For a given natural number k , a number n is called k perfect or k fold perfect if and only if the sum of all positive divisor s of n the divisor function , n is equal to kn a number is thus perfectnumberperfect if and only if it is 2 perfect. A number that is k perfect for a certain k is called a multiply perfectnumber. As of July 2004, k perfect numbers are known for each value of k up to 11. It can be proven that For a given prime number p , if n is p perfect and p does not divide n , then pn is p 1 perfect. This implies that an integer n is a 3 perfectnumber divisible by 2 but not by 4, if and only if n 2 is an odd perfectnumber , of which none are known. If 3 n is 4 k perfect and 3 does not divide n , then n is 3 k perfect. Smallest k perfect numbers The following table gives an overview of the smallest k perfect numbers for k 7 cf. Neil J. A. Sloane Sloane s http www.research.att.com njas sequences A007539 A007539 class wikitable k Smallest k perfectnumber Found by 1 1 number 1 ancient 2 6 number 6 ancient 3 120 number 120 ancient 4 30240 Ren Descartes , circa 1638 5 14182439040 Ren Descartes, circa 1638 6 154345556085770649600 Robert Daniel Carmichael , 1907 7 141310897947438348259849402738 485523264343544818565120000 TE Mason, 1911 For example, 120 is 3 perfect because the sum of the divisors of 120 is br 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 360 3 120. External links http wwwhomes.uni bielefeld.de achim mpn.html The Multiply Perfect Numbers page http primes.utm.edu glossary page.php?sort MultiplyPerfect The Prime Glossary Multiply perfect numbers Divisor classes navbox DEFAULTSORT Multiply PerfectNumber Category Integer sequences eo Multiplika perfekta nombro fr Nombre parfait multiple it Numero moltiplicativamente perfetto he ja fi Moninkertaisesti t ydellinen luku ... more details
A unitary perfectnumber is an integer which is the sum of its positive proper unitary divisor s, not including the number itself. A divisor d of a number n is a unitary divisor if d and n d share no common factors. Some perfectnumber s are not unitary perfect numbers, and some unitary perfect numbers are not regular perfect numbers. Thus, 60 number 60 is a unitary perfectnumber, because its unitary divisors, 1, 3, 4, 5, 12, 15 and 20 are its proper unitary divisors, and 1 3 4 5 12 15 20 60. The first few unitary perfect numbers are 6 number 6 , 60, 90 number 90 , 87360, 146361946186458562560000 OEIS id A002827 There are no odd unitary perfect numbers. This follows since one has 2 sup d n sup dividing the sum of the unitary divisors of an odd number where d n is the number of distinct prime divisors of n . One gets this because the sum of all the unitary divisors is a multiplicative function and one has the sum of the unitary divisors of a power of a prime number prime p sup a sup is p sup a sup 1 which is even for all odd primes p . Therefore, an odd unitary perfectnumber must have only one distinct prime factor, and it is not hard to show that a power of prime cannot be a unitary perfectnumber, since there are not enough divisors. It s not known whether or not there are infinitely many unitary perfect numbers. References cite book author Richard K. Guy authorlink Richard K. Guy title Unsolved Problems in Number Theory publisher Springer Verlag year 2004 isbn 0 387 20860 7 pages 84 86 Section B3. cite book title My Numbers, My Friends Popular Lectures on Number Theory authorlink Paulo Ribenboim author Paulo Ribenboim publisher Springer Verlag year 2000 isbn 0 387 98911 0 page 352 Divisor classes navbox Category Integer sequences numtheory stub eo Unuargumenta perfekta nombro fr Nombre parfait unitaire ... more details
In mathematics , an almost perfectnumber sometimes also called slightly defective number is a natural number n such that the sum of all divisor s of n the divisor function n is equal to 2 n 1, the sum of all proper divisors of n, s n n n , then being equal to n 1. The only known almost perfect numbers are powers of 2 with non negative exponents OEIS A000079 . Therefore the only known odd almost perfectnumber is 2 sup 0 sup 1, and the only known even almost perfect numbers are those of the form 2 sup k sup for some positive number k however, it has not been shown that all almost perfect numbers are of this form. Almost perfect numbers are also known as least deficient numbers. References Richard K. Guy Guy, R. K. , Almost Perfect, Quasi Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers. B2 in Unsolved Problems in Number Theory, 2nd ed. New York Springer Verlag, pp. 16 and 45 53, 1994. Singh, S., Fermat s Enigma The Epic Quest to Solve the World s Greatest Mathematical Problem. New York Walker, p. 13, 1997. External links mathworld urlname AlmostPerfectNumber title Almost perfectnumber Divisor classes navbox numtheory stub Category Divisor function Category Integer sequences eo Preska perfekta nombro fr Nombre presque parfait he it Numero lievemente difettivo nl Bijna perfect getal ru sl Skoraj popolno tevilo fi L hes t ydellinen luku sv N stan perfekt tal vi S g n ho n thi n thi u ... more details
In number theory , a perfect totient number is an integer that is equal to the sum of its iterated totient s. That is, we apply the totient function to a number n , apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers if the sum equals n , then n is a perfect totient number. Or to put it algebraically, if math n sum i ... such that math displaystyle varphi c n 2, math then n is a perfect totient number. The first few perfect totient numbers are 3 number 3 , 9 number 9 , 15 number 15 , 27 number 27 , 39 number 39 , 81 number 81 , 111 number 111 , 183 number 183 , 243 number 243 , 255 number 255 , 327 number 327 , 363 number 363 , 471, 729 number 729 , 2187, 2199, 3063, 4359, 4375, ... OEIS id A082897 . For example ... of perfect totient numbers if p 4× 3 sup k sup 1 is prime, then 3 p is a perfect totient number. The values of k leading to perfect totient numbers in this way are 0, 1, 2, 3, 6, 14, 15, 39, 201, 249, 1005, 1254, 1635, ... OEIS id A005537 . More generally if p is a prime number greater than 3, and 3 p is a perfect totient number, then p 1 mod 4 Mohan and Suryanarayana 1982 . Not all p of this form lead to perfect totient numbers for instance, 51 is not a perfect totient number. Iannucci et al. 2003 showed that if 9 p is a perfect totient number then p is a prime of one of three specific forms listed in their paper. It is not known whether there are any perfect totient numbers of the form ..., T. title Perfect totient number journal The Mathematics Student volume 43 year 1975 page 178 id MathSciNet id 0447089 PlanetMath attribution id 8741 title Perfect Totient Number Category Integer ..., and 216 72 24 8 4 2 1 327. Multiples and powers of three It can be observed that many perfect totient are multiples of 3 in fact, 4375 is the smallest perfect totient number that is not divisible by 3. All powers of 3 are perfect totient numbers, as may be seen by induction using the fact that math ... more details
see also Perfection disambiguation wiktionary perfect Perfection is a philosophical concept. Perfect may also refer to Music Perfect interval , a type of interval used in music Perfect musician Perfect band , a band from Poland Perfect Fairground Attraction song Perfect Fairground Attraction song , 1988 single Perfect Hedley song Perfect Hedley song , 2010 single Perfect Sara Evans song Perfect Sara Evans song Perfect Simple Plan song Perfect Simple Plan song a single from their debut album No Pads, No Helmets...Just Balls Perfect The Smashing Pumpkins song Perfect The Smashing Pumpkins song Perfect Vanessa Amorosi song Perfect Vanessa Amorosi song , 2008 debut international single Perfect Flyleaf song Perfect Flyleaf song Perfect Princess Superstar song Perfect Princess Superstar song Perfect Exceeder , a collaboration between Mason and Princess Superstar Fuckin Perfect by Pink singer Pink from Greatest Hits... So Far Perfect Records , a record label The Perfect , a song by The Killing Tree from The Romance of Helen Trent album The Romance Of Helen Trent perfecT , an album by Sam Shaber Perfect , an album by True Faith band True Faith , and a song from that album Perfect , a song by Alexandra ... Perfect , a song by Alanis Morissette from Jagged Little Pill Perfect , a song by John Cale from blackAcetate Perfect , a song by LIGHTS from Songs from Instant Star Four Perfect , a song by Depeche Mode from Sounds of the Universe Perfect , a song by Julia Murney off her album I m Not Waiting Perfect , a song by The The Film Perfect film Perfect film Mathematics PerfectnumberPerfect graph Perfect group Perfect lattice same as perfect form Perfect space Perfect matrix Perfect power Computer Science Perfect computer science , a specification language Perfect Developer , a tool for developing ... Perfect flowers have both male androecium and female gynoecium reproductive structures Linguistics Perfect grammar Perfect , a combined tense and aspect Religion Cathar Perfect , a Cathar priest Cassandra ... more details
Perfect square may refer to Mathematics Square number , a number that is a product of some integer with itself, e.g. 9 is a square number, its square root is 3 Perfect square dissection , a dissection of a geometric square into smaller squares, all of different sizes Perfect square trinomials , a square is also a prefect square. Music Perfect Square , a live recording by the band R.E.M. disambig ... more details
In mathematics , in the field of topology , perfect spaces are spaces that have no isolated point s. In such spaces ... perfect space is also used, incompatibly, to refer to other properties of a topological space, such as being .... In this article, a space which is not perfect will be referred to as imperfect . Examples and nonexamples The real line math mathbb R math is a connected perfect space, while the Cantor space 2 sup &omega sup and Baire space &omega sup &omega sup are perfect, totally disconnected zero dimensional ... . Any set with more than one point admits a perfect topology the indiscrete topology . Imperfection of a space Define the imperfection of a topological space to be the number of isolated points. This is a cardinal invariant i.e., a mapping which assigns to each topological space a cardinal number such that homeomorphic spaces get assigned the same number. A space is perfect if and only if it has imperfection zero. Closure properties Every nonempty perfect space has subsets which are imperfect in the subspace topology, namely the singleton sets. However, any open subspace of a perfect space is perfect. Perfection is a local property of a topological space a space is perfect if and only if every point in the space admits a basis of neighborhoods each of which is perfect in the subspace ... union math coprod i X i math is perfect if and only if each math X i math is perfect. The Cartesian product of a family math X i i in I math is perfect in the product topology if and only if at least one of the following holds i At least one math X i math is perfect. ii math I emptyset .... A continuous image, and even a quotient, of a perfect space need not be perfect. For example ... if x 0 and f x 1 if x 0. However, every image of a perfect space under an injective continuous map is perfect. Connection with other topological properties It is natural to compare the concept of a perfect ... singleton set is closed. A T sub 1 sub space is perfect if and only if every point of the space is an limit ... more details
Crystal line materials mainly metal s and alloy s, but also stoichiometry stoichiometric salt s and other materials are made up of solid regions of ordered matter atoms placed in one of a number of ordered formations called Bravais lattice s . These regions are known as crystals. A perfect crystal is one that contains no point, linear, or planar imperfections. There are a wide variety of crystallographic defect s. The hypothetical concept of a perfect crystal is important in the basic formulation of the laws of thermodynamics . In crystallography , the phrase perfect crystal can be used to mean no line or planar defects , as it is difficult to measure small quantities of point defects in an otherwise defect free crystal. Imperfections are created due to gravity. In space and in zero gravity environments perfect crystals can be created as on the International Space Station . ref http www.newscientisttech.com article dn12467 magnetic gravity trick grows perfect crystals.html ref References reflist Category Crystals cs Ide ln krystal ja pl Kryszta doskona y ... more details
A perfect ruler of length math n math is a ruler with a subset of the integer markings math 0,a 2, cdots,a n subset 0,1,2, ldots,n math that appear on a regular ruler. The defining criterion of this subset is that there exists an math m math such that any positive integer math k leq m math can be expressed uniquely as a difference math k a i a j math for some math i,j math . This is referred to as an math m math perfect ruler. A 4 perfect ruler of length math 7 math is given by math 0,1,3,7 math . To verify this, we need to show that every number math 1,2,3,4 math can be expressed as a difference of two numbers in the above set math 1 1 0 math math 2 3 1 math math 3 3 0 math math 4 7 3 math An Optimization mathematics optimal perfect ruler is one where for a fixed value of math n math the value of math a n math is minimized. See also Golomb ruler PlanetMath attribution id 1620 title perfect ruler Category combinatorics ... more details
The Perfect Couple may refer to The Perfect Couple film The Perfect Couple film , a 2007 South Korean film The Perfect Couple The Inside The Perfect Couple The Inside , an episode of The Inside The Perfect Couple The O.C. The Perfect Couple The O.C. , an episode of The O.C. The Perfect Couple , a song by Paul Heaton from Fat Chance album Fat Chance See also A Perfect Couple , a 1979 film directed by Robert Altman Perfect Couples , a 2010 2011 American sitcom disambig vi The Perfect Couple ... more details
Perfect Life may refer to Perfect Life Levinhurst album Perfect Life Levinhurst album , 2004 Perfect Life Yoga Lin album Perfect Life Yoga Lin album , 2011 Perfect Life film Perfect Life film , a 2008 Chinese Hong Kong film by Emily Tang disambiguation ... more details
Perfect Timing may refer to Perfect Timing McAuley Schenker Group album Perfect Timing McAuley Schenker Group album , 1987 Perfect Timing Boo & Gotti album Perfect Timing Boo & Gotti album , 2003 Perfect Timing Outlawz album Perfect Timing Outlawz album , 2011 disambiguation ... more details
Perfect Symmetry may refer to Perfect Symmetry Keane album Perfect Symmetry Keane album , or the title song Perfect Symmetry tour , a concert tour by Keane Perfect Symmetry Fates Warning album Perfect Symmetry Fates Warning album See also Symmetry , a harmonious proportionality, or patterned self similarity disambig es Perfect Symmetry it Perfect Symmetry nl Perfect Symmetry pl Perfect Symmetry ... more details
Interval music Number for more details , and the perfect fifth often abbreviated P5 is a fifth spanning ... scale chromatic circle which considers nearness not as adjacency but as the number of perfect ...Image Perfect fifth on C.png thumb right Perfect fifth audio Perfect fifth on C.mid Play equal tempered and audio Just perfect fifth on C.mid Play just. Infobox Interval main interval name perfect fifth inverse perfect fourth complement perfect fourth other names diapente abbreviation P5 semitones 7 ... just intonation 702 Image Perfect5s.PNG right thumb Examples of perfect fifth intervals In classical ... semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones ... fifth s span the same number of staff positions, but consist of a different number of semitones six and eight . The perfect fifth may be derived from the Harmonic series music harmonic series as the interval ... note is a perfect fifth above the tonic music tonic note. The perfect fifth is more consonance ... inversion is the perfect fourth . Alternative definitions The term perfect identifies the perfect fifth as belonging to the group of perfect intervals including the unison , perfect fourth and octave ... , p. 15. ISBN 0 393 95480 3. Octaves, perfect intervals, thirds, and sixths are classified as being ... of the term is not in all contexts compatible with the definition of perfect fifth ... sounds severely dissonant and can hardly be qualified as perfect , if this term is interpreted as highly ... or meantone temperament is actually not a perfect fifth but a diminished sixth for instance G Music sharp E Music flat . Perfect intervals are also defined as those natural intervals whose inversion music inversions are also perfect, where natural, as opposed to altered, designates those intervals ... from C to C, D, E, F, G, A, B, C, with no sharps or flats this definition leads to the perfect intervals being only the unison , perfect fourth fourth , fifth, and octave , without appealing to degrees ... more details
Perfect Skin may refer to Perfect Skin Lloyd Cole and the Commotions song Perfect Skin Lloyd Cole and the Commotions song Perfect Skin The 69 Eyes song Perfect Skin The 69 Eyes song dab ... more details
Perfect Strangers may refer to Perfect Strangers 1945 film Perfect Strangers 1945 film , a film starring Robert Donat and Deborah Kerr Perfect Strangers 1950 film Perfect Strangers 1950 film , a film starring Ginger Rogers Perfect Strangers 1984 film Perfect Strangers 1984 film , a film starring Anne Carlisle and Brad Rijn Perfect Strangers 2003 film Perfect Strangers 2003 film , a film starring Sam Neill Perfect Strangers 2004 film Perfect Strangers 2004 film , a film starring Rob Lowe and Anna Friel Perfect Strangers U.S. TV series Perfect Strangers U.S. TV series , a 1986 1993 US television sitcom starring Mark Linn Baker and Bronson Pinchot Perfect Strangers UK TV series Perfect Strangers UK TV series , a 2011 BBC British television drama by Stephen Poliakoff Perfect Strangers album Perfect Strangers album , a 1984 album by Deep Purple Perfect Strangers Deep Purple song Perfect Strangers Deep Purple song Perfect Strangers INXS song Perfect Strangers INXS song Invincible Vol. 3 Perfect Strangers , a trade paperback in the Invincible comics Invicible comic book series See also Perfect Stranger disambiguation disambiguation de Perfect Strangers it Perfect Strangers nl Perfect Strangers fi Perfect Strangers t smennyssivu ... more details
In mathematics, a perfect lattice or perfect form is a Lattice group lattice in a positive definite real vector space, that is determined by the set S its minimal vectors in the sense that there is only one positive definite quadratic form taking value 1 at all points of S . A strongly perfect lattice is one whose minimal vectors form a spherical 4 design. Perfect lattices were introduced by harvtxt Korkine Zolotareff 1877 . harvtxt last Voronoi year 1908 proved that a lattice is extreme if and only if it is both perfect and eutactic . The number of perfect lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8 is given by 1, 1, 1, 2, 3, 7, 33, 10916 OEIS id A004026 . harvtxt Conway Sloane 1988 summarize the properties of perfect lattices of dimension up to 7. harvtxt Sikiri Sch rmann Vallentin 2007 verified that the list of 10916 perfect lattices in dimension 8 found by Martinet and others is complete. References Citation last1 Conway first1 John Horton author1 link John Horton Conway last2 Sloane first2 N. J. A. author2 link Neil Sloane title Low dimensional lattices. III. Perfect forms jstor 2398316 mr 953277 year 1988 journal Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences issn 0962 8444 volume 418 issue 1854 pages 43 80 cite journal jstor 2398351 Citation last1 Korkine last2 Zolotareff title Sur les formes quadratique positives doi 10.1007 BF01442667 year 1877 journal Mathematische Annalen issn 0025 5831 volume 11 pages 242 292 Citation last1 Martinet first1 Jacques title Perfect lattices in Euclidean spaces url http books.google.com books?id gd9CcFclBRIC publisher Springer Verlag location Berlin, New York series Grundlehren der Mathematischen Wissenschaften Fundamental Principles of Mathematical Sciences isbn 978 3 540 44236 ... Achill last3 Vallentin first3 Frank title Classification of eight dimensional perfect forms arxiv ... 97 178 External links http www.math.uni magdeburg.de lattice geometry List of perfect lattices in dimension ... more details
generally, a ring mathematics ring of characteristic p p a prime number prime is called perfect if the Frobenius ... is a prime number every algebraically closed field the union of perfect fields fields algebraic over a perfect field. In fact, most fields that appear in practice are perfect. The imperfect case arises ...In algebra , a field mathematics field k is said to be perfect if any one of the following equivalent conditions holds Every irreducible polynomial over k has distinct roots. Every polynomial over k is separable polynomial separable . Every finite extension of k is separable extension separable . Every algebraic extension of k is separable. Either k has characteristic algebra characteristic 0, or, when k has characteristic p 0, every element of k is a Power mathematics p th power . Either k has characteristic ... of characteristic zero and all finite field s are perfect. Perfect fields are significant because ... of perfect fields are every field of characteristic zero, e.g. the field of rational numbers ... , because the latter is perfect. An example of an imperfect field is the field math k X math of all ... has no p th root in k X . Field extension over a perfect field Any finitely generated field extension over a perfect field is separably generated field extension separably generated . ref Matsumura, Theorem 26.2 ref Perfect closure and perfection The first condition says that, in characteristic p , a field adjoined with all p sup r sup th roots r &ge 1 is perfect it is called the perfect closure of k ... , the perfect closure of a ring A of characteristic p is a perfect ring A sub p sub of characteristic p together with a ring homomorphism u A A sub p sub such that for any other perfect ring B of characteristic ... through u i.e. v fu . The perfect closure always exists the proof involves adjoining p th roots ... used for the perfect closure . In other words, the perfection R A of A is a perfect ring of characteristic p together with a map R A A such that for any perfect ring B of characteristic p equipped ... more details
Perfect Stranger may refer to The Perfect Stranger , an autobiography by P. J. Kavanagh Perfect Stranger film Perfect Stranger film , a 2007 suspense film The Perfect Stranger film The Perfect Stranger film , a 2005 Christian film Perfect Stranger band , an American country music quartet Perfect Stranger artist , a performing name for the Israeli psychedelic trance artist Yuli Fershtat Perfect Stranger album Perfect Stranger album , a 2008 album by K Maro A Perfect Stranger , a 1981 romance novel by Danielle Steel Danielle Steel s A Perfect Stranger , a 1994 film The Perfect Stranger , a 1982 album by Jesse Colin Young Desconocida or Perfect Stranger , an album by Marta Sanchez Boulez Conducts Zappa The Perfect Stranger , a 1984 album by Frank Zappa Perfect Stranger song Perfect Stranger song , a 2010 song by Magnetic Man See also Perfect Strangers disambiguation disambig it Perfect Stranger ... more details
a clique of three vertices. In this graph and each of its induced subgraphs the chromatic number equals the clique number, so it is a perfect graph. In graph theory , a perfect graph or a Berge graph is a graph mathematics graph in which the Graph coloring chromatic number of every induced subgraph ..., the clique number provides a lower bound for the chromatic number, as all vertices in a clique must be assigned distinct colors in any proper coloring. The perfect graphs are those for which this lower ... graphs, the chromatic number and clique number can differ e.g., a cycle of length 5 requires three colors in any proper coloring but its largest clique has size 2. Perfect graphs include many important .... For instance, in all perfect graphs, the graph coloring problem , maximum clique problem , and maximum ... , can be expressed in terms of the perfection of certain associated graphs. The theory of perfect ... that the complement graph complement of a bipartite graph is perfect this result can also be viewed ... relating matchings and vertex covers in bipartite graphs. The first use of the phrase perfect graph ... similar results by defining perfect graphs and conjecturing a characterization of these graphs that was later proven as the Strong Perfect Graph Theorem. Families of graphs that are perfect Some of the more well known perfect graphs are bipartite graph s The line graph s of bipartite graphs see K nig ... order , and an edge between any two comparable elements wheel graph s with an odd number of vertices ... induced subgraph trivially perfect graph s in every induced subgraph the size of the largest independent set equals the number of maximal cliques Meyniel graphs every cycle of odd length at least 5 has at least 2 chords strongly perfect graphs every induced subgraph has an independent set intersecting all its maximal cliques very strongly perfect graphs in every induced subgraph, every vertex belongs to an independent set meeting all maximal cliques . Characterizations and the perfect graph ... more details
Perfect Circle can refer to Savrseni Krug The Perfect Circle , a 1997 movie by Bosnian director Ademir Kenovic. Perfect Circle novel Perfect Circle novel , 2004 novel by Sean Stewart Perfect Circle song Perfect Circle song , song from R.E.M. s debut album Murmur A Perfect Circle , rock band The Perfect Circle Co., U.S. manufacturer of piston ring s, now part of the Dana Corporation disambig ru Perfect Circle ... more details
Perfect Gentleman may refer to Perfect Gentleman Wyclef Jean song Perfect Gentleman Wyclef Jean song Perfect Gentleman song Perfect Gentleman song , by the German power metal band Helloween A Quiver Full of Arrows The Perfect Gentleman The Perfect Gentleman , a short story by Jeffrey Archer The Imperfect Lady 1935 film The Perfect Gentleman , a 1935 film starring Frank Morgan See also Perfect Gentlemen , an American R&B trio disambig ... more details
Infobox single Name Perfect Situation Cover Perfect Situation.jpg Artist Weezer Album Make Believe Weezer album Make Believe Released December 2005 Format Compact Disc CD Recorded 2004 Genre Pop punk , emo Length 4 14 Label XL Recordings XL Writer Rivers Cuomo Producer Rick Rubin Last single We Are All on Drugs br 2005 This single Perfect Situation br 2005 Next single This Is Such a Pity br 2006 Perfect Situation is a song by American alternative rock band Weezer . It was released as the band s third single from their fifth album, Make Believe Weezer album Make Believe , following Beverly Hills song Beverly Hills and We Are All on Drugs . The song is also one of their most successful songs to date as well, topping the Billboard Alternative Songs Modern Rock Tracks for four weeks, outlasting the first single from Make Believe , Beverly Hills . Radio edit The radio edit of this song features a shortened intro, a synth track on the first and second chorus the album version only has it on the second chorus , a reworked oh oh chorus and the added backup vocals of perfect situation over the outro. The radio edit is eight seconds shorter than the album version. The reworked chorus that appears in the radio edit was one of two ways Cuomo originally wrote the song. When touring in summer 2005, when the band prompted the crowd to sing along, they oddly enough sung it in the other way Cuomo ... of Perfect Situation showing the fictional name Weeze . Personnel Rivers Cuomo Lead vocalist lead ... production External links http www.weezernet.com index.php?page lyrics&lid 234 Lyrics for Perfect Situation youtube jwv iRvyDZg Perfect Situation Official music video start box succession box before ... List of number one modern rock hits United States number one single years January 28, 2006 February ... Category 2005 singles Category Billboard Alternative Songs number one singles Category Songs written ... 2000s rock song stub ca Perfect Situation es Perfect Situation gl Perfect Situation it Perfect Situation ... more details
Perfect Match may refer to Perfect Match American game show Perfect Match American game show , a game show where married couples tried to answer their spouse s questions to win money Perfect Match Australian game show Perfect Match Australian game show Perfect Match British game show Perfect Match British game show Perfect Match 1994 game show Perfect Match 1994 game show , a 1994 ESPN game show, with questions based on sports figures Perfect Match novel Perfect Match novel , a 2002 novel by Jodi Picoult perfectmatch.com , a dating website Perfect Match , a song by Dev from the album The Night the Sun Came Up See also A Perfect Match disambiguation disambig ... more details
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