For text reconstruction Conjecture textual criticism No footnotes date August 2010 A conjecture is a Proposition philosophy proposition that is Formal proof unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term conjecture in scientific philosophy . Conjecture is contrasted by hypothesis hence theory , axiom , principle , which is a testable statement based on accepted grounds. In mathematics , a conjecture is an unproven proposition or theorem that appears correct. Famous conjectures Beal s conjecture The Poincar theorem proven by Grigori Perelman Goldbach s conjecture The Riemann hypothesis The Collatz conjecture The Maldacena conjecture The Langlands program is a far reaching web of these ideas of unifying conjecture s that link different .... In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture s veracity, since a single counterexample would immediately bring down the conjecture. Conjectures disproven through counterexample are sometimes referred to as false conjectures cf. P lya conjecture . Mathematical journals sometimes publish the minor results of research teams having extended a given search farther than previously done. For instance, the Collatz conjecture ... contributions to formal mathematics. Use of conjectures in conditional proofs Sometimes a conjecture ... results. For example, the Riemann hypothesis is a conjecture from number theory that amongst other ... which are contingent on the truth of this conjecture. These are called conditional proof s the conjectures ... the truth or falsity of conjectures of this type. Undecidable conjectures Not every conjecture ... also Hypothesis Hypotheticals List of conjectures External links Wiktionary conjecture http garden.irmacs.sfu.ca ... de Vermutung Mathematik es Conjetura eo Konjekto matematiko fa fr Conjecture gd Baralachas ... Konjektur nl Vermoeden ja pl Przypuszczenie pt Conjectura ru simple Conjecture sk Domnienka ... more details
In mathematics, Kummer s conjecture is either of two the conjectures made by Ernst Eduard Kummer The Kummer Vandiver conjecture about class numbers of cyclotomic fields Kummer s conjecture about the Kummer sum mathematical disambiguation ... more details
The mathematician Leonard Euler 1707 1783 made several different conjectures which are all called Euler s conjecture Euler s sum of powers conjecture Euler s conjecture Waring s problem disambig Category Mathematical disambiguation th ... more details
In mathematics , Jean Pierre Serre has suggested a number of conjectural or formerly conjectural results The Serre modularity conjecture concerning Galois representations Ribet s theorem , formerly known as Serre s epsilon conjecture. The Quillen Suslin theorem , formerly known as Serre s conjecture Serre s multiplicity conjectures in commutative algebra Serre s conjecture II algebra Serre s Conjecture II concerning the Galois cohomology of linear algebraic group s. mathdab Category Conjectures ... more details
In mathematics , there are a number of so called Deligne conjectures , provided by Pierre Deligne . These are independent conjecture s in various fields of mathematics. The Deligne conjecture in deformation theory is about the operad ic structure on Hochschild cohomology . It was proved by Kontsevich Yan Soibelman Soibelman , McClure Smith and others. It is of importance in relation with string theory . The Deligne conjecture on special values of L functions is a formulation of the hope for Algebraic number algebraicity of L n where L is an L function and n is an integer in some set depending on L . There is a Deligne conjecture on 1 motives arising in the theory of motive algebraic geometry motives in algebraic geometry . There is a Gross Deligne conjecture in the theory of complex multiplication . There is a Deligne conjecture on monodromy , also known as the weight monodromy conjecture , or purity conjecture for the monodromy filtration . There is E7 Lie algebra Deligne conjecture in the representation theory of the exceptional Lie group s. There is a Deligne Langlands conjecture of historical importance in relation with the development of the Langlands philosophy . disambiguation Category Algebraic geometry Category Conjectures ... more details
There are several conjectures in mathematics by David Mumford . Mumford s conjecture about reductive groups, now called Haboush s theorem . The Mumford conjecture on the cohomology of the stable mapping class group , proved by Ib Madsen and Michael Weiss. The Manin Mumford conjecture about Jacobians of curves, proved by Michel Raynaud. mathdab ... more details
The term Weil conjecture may refer to The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne and others. The Modularity theorem Taniyama Shimura Weil conjecture about elliptic curves, proved by Wiles and others. The Weil conjecture on Tamagawa numbers about the Tamagawa number of an algebraic group , proved by Kottwitz and others. The Hasse Weil conjecture about zeta functions. mathdab ... more details
There are two main conjectures known as the Hadwiger conjecture or Hadwiger s conjecture Hadwiger conjecture graph theory , a relationship between the number of colors needed by a given graph and the size of its largest clique minor Hadwiger conjecture combinatorial geometry that for any n dimensional convex body, at most 2 sup n sup smaller homothetic bodies are necessary to contain the original See also Hadwiger Nelson problem on the chromatic number of unit distance graphs in the Euclidean plane Hadwiger s theorem characterizing measure functions in Euclidean spaces disambig ... more details
The prolific mathematician Paul Erd s and his various collaborators made many famous mathematical conjecture s, over a wide field of subjects. Some of these are the following The Cameron Erd s conjecture on sum free sets of integers, proved by Ben J. Green Ben Green . The Erd s Burr conjecture on Ramsey numbers of graphs. The Erd s Faber Lov sz conjecture on coloring unions of cliques. The Erd s Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity. The Erd s Gy rf s conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3. The Erd s Hajnal conjecture that in a family of graphs defined by an excluded induced ..., Discrete Applied Mathematics 25 1989 37 52 The Restricted sumset Erd s Heilbronn conjecture in combinatorial ... Dias da Silva and Y.O. Hamidoune in 1994. The Erd s Lov sz conjecture on weak strong delta systems ... Erd s Mollin Walsh conjecture on consecutive triples of powerful numbers. The Erd s Menger conjecture ... Aharoni and Eli Berger The Erd s Selfridge conjecture that a covering set contains at least one odd member. The Erd s Stewart conjecture on the Diophantine equation n 1 p sub k sub sup a sup p sub k 1 sub sup b sup solved by Luca, MR 2001g 11042 The Erd s Straus conjecture on the Diophantine equation 4 n 1 x 1 y 1 z . The Erd s conjecture on arithmetic progressions in sequences with divergent sums of reciprocals. The Erd s Woods number Erd s Woods conjecture on numbers determined by the set of prime divisors of the following k numbers. The Erd s Szekeres conjecture ... Tur n conjecture on additive bases of natural numbers. A conjecture on Sylvester s sequence quickly growing integer sequences with rational reciprocal series . A conjecture on equitable coloring s proven in 1970 by Andr s Hajnal and Endre Szemer di and now known as the Hajnal Szemer di theorem . A conjecture ... Conjectures Erdos conjecture Category Mathematical disambiguation Erdos conjecture Category Paul Erd s ... more details
In mathematics, there are several conjectures made by Emil Artin Artin conjecture L functions Artin s conjecture on primitive roots The now proved conjecture that finite fields are quasi algebraically closed see Chevalley Warning theorem . The now disproved conjecture that any algebraic form over the p adics of degree d in more than d sup 2 sup variables represents zero. For this see Ax Kochen theorem or Brauer s theorem on forms . Artin had also conjectured Hasse s theorem on elliptic curves disambig DEFAULTSORT Artin Conjecture Category Analytic number theory Category Algebraic number theory Category Conjectures fr Conjecture d Artin ... more details
In number theory , Lemoine s conjecture , named after mile Lemoine , also known as Levy s conjecture , after Hyman Levy , states that all odd integer s greater than 5 can be represented as the sum of an odd prime number and an even semiprime . To put it algebraically, 2 n 1 p 2 q always has a solution in primes p and q not necessarily distinct for n 2. The Lemoine conjecture is similar to but stronger than Goldbach s weak conjecture . For example, 47 13 2 17 37 2 5 41 2 3 43 2 2. OEIS id A046927 counts how many different ways 2 n 1 can be represented as p 2 q . According to MathWorld , the conjecture has been verified by Corbitt up to 10 sup 9 sup . The conjecture was posed by mile Lemoine in 1895, but in more recent years came to be attributed to Hyman Levy who pondered it in the 1960s. See also mile Lemoine Lemoine s conjecture and extensions Lemoine s conjecture and extensions References Emile Lemoine, L interm diare des math maticiens , 1 1894 , 179 ibid 3 1896 , 151. H. Levy, On Goldbach s Conjecture , Math. Gaz. 47 1963 274 L. Hodges, A lesser known Goldbach conjecture , Math. Mag. , 66 1993 45 47. John O. Kiltinen and Peter B. Young, Goldbach, Lemoine, and a Know Don t Know Problem , Mathematics Magazine , Vol. 58, No. 4 Sep., 1985 , pp. 195 203 http www.jstor.org stable 2689513?seq 7 Richard K. Guy , Unsolved Problems in Number Theory New York Springer Verlag 2004 C1 External links MathWorld title Levy s Conjecture urlname LevysConjecture http demonstrations.wolfram.com LevysConjecture Levy s Conjecture by Jay Warendorff, Wolfram Demonstrations Project . Category Additive number theory Category Conjectures about prime numbers it Congettura di Levy zh ... more details
In mathematics, the Shafarevich conjecture , named for Igor Shafarevich , may refer to The Tate Shafarevich conjecture that the Tate Shafarevich group is finite The Shafarevich conjecture that there are only finitely many isomorphism classes of abelian varieties of fixed dimension and fixed polarization degree over a fixed number field with good reduction outside a given finite set of places, now proved as Faltings theorem mathdab ... more details
nofootnotes date February 2010 Orphan date December 2009 In mathematics , the Nakai conjecture states that if V is a complex algebraic variety , such that its ring of differential operators is generated by the derivation algebra derivations it contains, then V is a smooth algebraic variety smooth variety . This is the conjectural converse to a result of Alexander Grothendieck . It is known to be true for algebraic curve s. The conjecture was proposed by the Japanese mathematician Yoshikazu Nakai. A consequence would be the Zariski Lipman conjecture , for a complex variety V with coordinate ring R if the derivations of R are a free module over R , then V is smooth. Sources Google Scholar results for http scholar.google.com scholar?q nakai 20conjecture&oe utf 8&rls com.ubuntu en US official&client firefox a&um 1&ie UTF 8&sa N&hl en&tab ws nakai conjecture Nakai s Conjecture for Varieties Smoothed by Normalization,William N. Traves, Proceedings of the American Mathematical Society, Vol. 127, No. 8 Aug., 1999 , pp. 2245 2248 DEFAULTSORT Nakai Conjecture Category Algebraic geometry Category Singularity theory Category Conjectures ... more details
In algebra the Dixmier conjecture , asked by harvtxt Dixmier 1968 loc problem 1 , is the conjecture that any endomorphism of a Weyl algebra is an automorphism. harvtxt Belov Kanel Kontsevich 2007 showed that the Dixmier conjecture generalized to Weyl algebras with more generators is equivalent to the Jacobian conjecture . References Citation last1 Dixmier first1 Jacques title Sur les alg bres de Weyl url http www.numdam.org item?id BSMF 1968 96 209 0 mr 0242897 year 1968 journal Bulletin de la Soci t Math matique de France volume 96 pages 209 242 Tsuchimoto, Yoshifumi. Endomorphisms of Weyl algebra and p curvatures . Osaka J. Math. 42 2005 , 435 452. Citation last1 Belov Kanel first1 Alexei last2 Kontsevich first2 Maxim title The Jacobian conjecture is stably equivalent to the Dixmier conjecture arxiv math 0512171 mr 2337879 year 2007 journal Moscow Mathematical Journal volume 7 issue 2 pages 209 218 Category Algebra Category Conjectures algebra stub ... more details
In mathematics , specifically geometric topology , the Borel conjecture asserts that an Aspherical space aspherical closed manifold is determined by its fundamental group , up to homeomorphism . It is a Rigidity mathematics rigidity conjecture, demanding that a weak, algebraic notion of equivalence namely, a homotopy homotopy equivalence imply a stronger, topological notion namely, a homeomorphism . Precise formulation of the conjecture Let math M math and math N math be closed manifold closed and Aspherical space aspherical topological manifold s, and let math f M to N math be a homotopy homotopy equivalence . The Borel conjecture states that the map math f math is homotopic to a homeomorphism ... conjecture implies that aspherical closed manifolds are determined, up to homeomorphism, by their fundamental groups. This conjecture is false if topological manifold s and homeomorphisms are replaced ... sum with an exotic sphere . The origin of the conjecture In a May 1953 letter to Jean Pierre Serre ... fundamental groups are homeomorphic. Motivation for the conjecture A basic question is the following ... manifold s is homotopic to an isometry in particular, to a homeomorphism. The Borel conjecture is a topological .... Relationship to other conjectures The Borel conjecture implies the Novikov conjecture for the special case in which the reference map math f M to BG math is a homotopy equivalence. The Poincar conjecture ... to math S 3 math . This is not a special case of the Borel conjecture, because math S 3 math is not aspherical. Nevertheless, the Borel conjecture for the Torus 3 torus math T 3 S 1 times S 1 times S 1 math implies the Poincar conjecture for math S 3 math . References F.T. Farrell, The Borel conjecture. Topology of high dimensional manifolds, No. 1, 2 Trieste, 2001 , 225 298, ICTP Lect. Notes, 9, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2002. M. Kreck, and W. L ck, The Novikov conjecture ... aar surgery borel.pdf The birth of the Borel conjecture , Extract from letter from Armand ... more details
No footnotes date January 2010 Legendre s conjecture , proposed by Adrien Marie Legendre , states that there is a prime number between n sup 2 sup and n 1 sup 2 sup for every positive integer n . The conjecture is one of Landau s problems 1912 and remains unsolved. The prime number theorem suggests the actual number of primes between n sup 2 sup and n 1 sup 2 sup OEIS A014085 is about n log n , i.e. about as many as the Prime counting function number of primes less than or equal to n . If Legendre s conjecture is true, the prime gap gap between any two successive primes would be math O sqrt p math . In fact the conjecture follows from Andrica s conjecture . Harald Cram r Cram r s conjecture conjectured that the gap is always much smaller, math O log 2 p math if Cram r s conjecture is true, Legendre s conjecture would follow. Cram r also proved that the Riemann hypothesis implies a weaker bound of math O sqrt p log p math on the size of the largest prime gaps. Legendre s conjecture implies that at least one prime can be found in every revolution of the Ulam spiral . Because the conjecture follows from Andrica s conjecture, it suffices to check that each prime gap starting at p is smaller than math 2 sqrt p. math A table of maximal prime gaps shows that the conjecture holds to 10 sup 18 sup . A counterexample near 10 sup 18 sup would require a prime gap fifty million times the size of the average gap. Legendre s conjecture follows from Oppermann s conjecture . See also Brocard s conjecture External links mathworld urlname LegendresConjecture title Legendre s conjecture Category Conjectures about prime numbers Category Unsolved problems in mathematics Numtheory stub ca Conjectura de Legendre de Legendresche Vermutung es Conjetura de Legendre fr Conjecture de Legendre it Congettura di Legendre nl Vermoeden van Legendre pt Conjectura de Legendre zh ... more details
This page concerns mathematician Sergei Novikov s topology conjecture. For astrophysicist Igor Novikov s conjecture regarding time travel, see Novikov self consistency principle . The Novikov conjecture is one of the most important unsolved problems in topology . It is named for Sergei Novikov mathematician Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomial s in the Pontryagin class es of a manifold mathematics manifold , arising from the fundamental group . According to the Novikov conjecture, the higher signatures , which are certain numerical invariants of smooth manifolds, are homotopy invariants. The conjecture has been proved for finitely generated abelian groups . It is not yet known whether the Novikov conjecture holds true for all groups. There are no known counterexamples to the conjecture. Precise formulation of the conjecture Let G be a discrete group and BG its classifying space , which is a Eilenberg ... bundle. The Novikov conjecture states that the higher signature is a homotopy invariant for every such map f and every such class x . Connection with the Borel conjecture The Novikov conjecture is equivalent to the rational injectivity of the assembly map in L theory . The Borel conjecture ... chapter Manifold aspects of the Novikov conjecture pages 195 224 J. Milnor and Jim Stasheff J. D. Stasheff ... jmr NC.html Novikov Conjecture Bibliography http www.maths.ed.ac.uk aar books novikov1.pdf Novikov Conjecture 1993 Oberwolfach Conference Proceedings, Volume 1 http www.maths.ed.ac.uk aar books novikov2.pdf Novikov Conjecture 1993 Oberwolfach Conference Proceedings, Volume 2 http www.math.uni muenster.de u lueck publ lueck owsemfinalextract.pdf 2004 Oberwolfach Seminar notes on the Novikov Conjecture pdf http www.scholarpedia.org article Novikov conjecture Scholarpedia article by S.P. Novikov 2010 http www.map.him.uni bonn.de Novikov Conjecture The Novikov Conjecture at the Manifold Atlas ... more details
In mathematics, Nakayama s conjecture is a conjecture about Artinian ring s, introduced by harvs txt last Nakayama authorlink Tadasi Nakayama year 1958 . The generalized Nakayama conjecture is an extension to more general rings, introduced by harvs txt last Auslander last2 Reiten year 1975 . harvtxt Leuschke Huneke 2004 proved some cases of the generalized Nakayama conjecture. Nakayama s conjecture states that if all the modules of a minimal injective resolution of an Artin algebra R are injective and projective, then R is self injective. References Citation last1 Auslander first1 Maurice last2 Reiten first2 Idun title On a generalized version of the Nakayama conjecture url http www.jstor.org stable 2040102 id MR 0389977 year 1975 journal Proceedings of the American Mathematical Society issn 0002 9939 volume 52 pages 69 74 Citation last1 Leuschke first1 Graham J. last2 Huneke first2 Craig title On a conjecture of Auslander and Reiten url http dx.doi.org 10.1016 j.jalgebra.2003.07.018 doi 10.1016 j.jalgebra.2003.07.018 id MR 2052636 year 2004 journal Journal of Algebra issn 0021 8693 volume 275 issue 2 pages 781 790 Citation last1 Nakayama first1 Tadasi title On algebras with complete homology doi 10.1007 BF02941960 id MR 0104718 year 1958 journal Abhandlungen aus dem Mathematischen Seminar der Universit t Hamburg issn 0025 5858 volume 22 pages 300 307 Category Ring theory ... more details
In mathematics , the Seifert conjecture states that every nonsingular, continuous vector field on the 3 sphere has a closed orbit. It is named after Herbert Seifert . In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non existence as a conjecture. He also established the conjecture for perturbations of the Hopf fibration . The conjecture was disproven in 1974 by Paul Schweitzer , who exhibited a math C 1 math counterexample. Schweitzer s construction was then modified by Jenny Harrison in 1988 to make a math C 2 delta math counterexample for some math delta 0 math . The existence of smoother counterexamples remained an open question until 1993 when Krystyna Kuperberg constructed a very different math C infty math counterexample. Later this construction was shown to have real analytic and piecewise linear versions. References V. Ginzburg and B. G rel, http front.math.ucdavis.edu math.DG 0110047 A math C 2 math smooth counterexample to the Hamiltonian Seifert conjecture in math R 4 math , Ann. of Math. 2 158 2003 , no. 3, 953 976 J. Harrison, math C 2 math counterexamples to the Seifert conjecture , Topology 27 1988 , no. 3, 249 278. G. Kuperberg A volume preserving counterexample to the Seifert conjecture , Comment. Math. Helv. 71 1996 , no. 1, 70 97. K. Kuperberg A smooth counterexample to the Seifert conjecture , Ann. of Math. 2 140 1994 , no. 3, 723 732. G. Kuperberg and K. Kuperberg, http front.math.ucdavis.edu math.DS 9802040 Generalized counterexamples to the Seifert conjecture , Ann. of Math. 2 143 1996 , no. 3, 547 576. H. Seifert, Closed integral curves in 3 space and isotopic two dimensional deformations , Proc. Amer. Math. Soc. 1, 1950 . 287 302. P. A. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations , Ann. of Math. 2 100 1974 , 386 400. Further reading K. Kuperberg, http www.ams.org notices 199909 fea kuperberg.pdf Aperiodic dynamical systems . Notices Amer. Math. Soc. 46 1999 , no. 9 ... more details
for the conjecture about the Riemann zeta function Selberg s zeta function conjecture In mathematics, Selberg s conjecture , conjectures by harvs txt authorlink Atle Selberg last Selberg year 1965 loc p.13 , states that the eigenvalues of the Laplacian operator on Maass wave form s of congruence subgroups are at least 1 4. Selberg showed that the eigenvalues are at least 3 16. The generalized Ramanujan conjecture for the general linear group implies Selberg s conjecture. More precisely, Selberg s conjecture is essentially the generalized Ramanujan conjecture for the group GL sub 2 sub over the rationals at the infinite place, and says that the component at infinity of the corresponding representation is a principal series representation of GL sub 2 sub R rather than a complementary series representation . The generalized Ramanujan conjecture in turn follows from the Langlands functoriality conjecture , and this has led to some progress on Selberg s conjecture. References eom id s s130210 first S. last Gelbart Citation last1 Kim first1 Henry H. last2 Sarnak first2 Peter title Functoriality for the exterior square of GL sub 4 sub and the symmetric fourth of GL sub 2 sub . Appendix 2. doi 10.1090 S0894 0347 02 00410 1 mr 1937203 year 2003 journal Journal of the American Mathematical Society issn 0894 0347 volume 16 issue 1 pages 139 183 Citation last1 Selberg first1 Atle editor1 last Whiteman editor1 first Albert Leon title Theory of Numbers url http books.google.com books?id 6xAZAQAAIAAJ publisher American Mathematical Society location Providence, R.I. series Proceedings of Symposia in Pure Mathematics isbn 978 0 8218 1408 6 mr 0182610 year 1965 volume VIII chapter On the estimation of Fourier coefficients of modular forms pages 1 15 Category Automorphic forms ... more details
In the mathematical subject of knot theory , the Berge conjecture states that the only knot mathematics knot s in the 3 sphere which admit lens space Dehn surgery surgeries are Berge knot s. The conjecture and family of Berge knots is named after John Berge . Progress on the conjecture has been slow. Recently Yi Ni proved that if a knot admits a lens space surgery, then it is fibered knot fibered . Berge knots are fibered. External links Two blog posts in the weblog Low Dimensional Topology Recent Progress and Open Problems related to the Berge conjecture http ldtopology.wordpress.com 2007 11 19 the berge conjecture The Berge conjecture , by Jesse Johnson http ldtopology.wordpress.com 2008 06 30 knot complements covering knot complements Knot complements covering knot complements by Ken Baker References Yi Ni. Knot Floer homology detects fibred knots. Invent. Math. 170 2007 , no. 3, 577 608. Yi Ni. Corrigendum to http arxiv.org pdf 0808.0940v1 Knot Floer homology detects fibred knots pdf original ref link http arxiv.org abs 0808.0940 arXiv 0808.0940v1 Category Knot theory Category 3 manifolds knottheory stub ... more details
In combinatorics combinatorial mathematics , the Albertson conjecture is an unproven relationship between ... after Michael O. Albertson, a professor at Smith College , who stated it as a conjecture in 2007 ref According to harvtxt Albertson Cranston Fox 2009 , the conjecture was made by Albertson at a special ... publisher SIAM Activity group on Discrete Mathematics . ref The conjecture states that, among ... to the conjecture, it may be colored with fewer than n colors. It is straightforward to show that graphs ... to the endpoints of all crossing edges and then 4 color the remaining planar graph . Albertson s conjecture ... quantitative relationship. Specifically, a different conjecture of harvs first Richard K. last Guy ... formulation of the Albertson conjecture is that every n chromatic graph has crossing number at least ... This strengthened conjecture would be true if and only if both Guy s conjecture and the Albertson conjecture are true. The Albertson conjecture is vacuous truth vacuously true for n 4 K sub .... The case n 5 of Albertson s conjecture is equivalent to the four color theorem , that any ... than the one crossing of K sub 5 sub are the planar graphs, and the conjecture implies that these should all be at most 4 chromatic. Through the efforts of several groups of authors the conjecture ... Fox 2009 harvtxt Bar t T th 2010 . ref There is also a connection to the Hadwiger conjecture graph theory Hadwiger conjecture , an important open problem in combinatorics concerning the relationship ... minors in a graph. ref harvtxt Bar t T th 2009 . ref A variant of the Hadwiger conjecture, stated ... of K sub n sub if this were true, the Albertson conjecture would follow, because the crossing number ..., counterexamples to the Haj s conjecture are now known, ref harvtxt Catlin 1979 harvtxt Erd s Fajtlowicz 1981 . ref so this connection does not provide an avenue for proof of the Albertson conjecture ... Conjecture arxiv 0909.0413 journal Electronic Journal of Combinatorics volume 17 issue 1 page ... more details
In mathematics, the Lichnerowicz conjecture is a generalization of a conjecture introduced by harvs txt last Lichnerowicz authorlink Andr Lichnerowicz year 1944 . Lichnerowicz s original conjecture was that locally harmonic 4 manifolds are locally symmetric, and was proved by harvtxt Walker 1949 . The Lichnerowicz conjecture usually refers to the generalization that locally harmonic manifolds are flat or rank 1 locally symmetric. References Citation last1 Lichnerowicz first1 Andr title Sur les espaces riemanniens compl tement harmoniques url http www.numdam.org item?id BSMF 1944 72 146 0 id MR 0012886 year 1944 journal Bulletin de la Soci t Math matique de France issn 0037 9484 volume 72 pages 146 168 Citation last1 Szab first1 Z. I. title The Lichnerowicz conjecture on harmonic manifolds url http projecteuclid.org getRecord?id euclid.jdg 1214444087 id MR 1030663 year 1990 journal Journal of Differential Geometry issn 0022 040X volume 31 issue 1 pages 1 28 Citation last1 Walker first1 A. G. title On Lichnerowicz s conjecture for harmonic 4 spaces doi 10.1112 jlms s1 24.1.21 id MR 0030280 year 1949 journal Journal of the London Mathematical Society. Second Series issn 0024 6107 volume 24 pages 21 28 Category Riemannian geometry ... more details
Beal s conjecture is a conjecture in number theory proposed by Andrew Beal in about 1993 a similar conjecture was suggested independently at about the same time by Andrew Granville . While investigating generalizations of Fermat s last theorem in 1993, Beal formulated the following conjecture If math A x B y C z, math where A , B , C , x , y , and z are positive integers with x , y , z 2 then A , B , and C must have a common prime divisor factor . Beal has offered a prize of USD US 100,000 for a proof of his conjecture or a counterexample . ref http www.math.unt.edu mauldin beal.html The Beal Conjecture Bot generated title ref Examples To illustrate, the solution 3 sup 3 sup 6 sup 3 sup 3 sup 5 sup has bases with a common factor of 3, and the solution 7 sup 6 sup 7 sup 7 sup 98 sup 3 sup has bases with a common factor of 7. Indeed the equation has infinitely many solutions, including for example math left a left a m b m right right m left b left a m b m right right m left a m b m right ... to the conjecture, since the bases all have the factor math a m b m math in common. The example 7 sup 3 sup 13 sup 2 sup 2 sup 9 sup shows that the conjecture is false if one of the exponents ... arithmetic , this conjecture has been verified for all values of all six Variable mathematics variables up to 1000. ref http www.norvig.com beal.html Beal s Conjecture A Search for Counterexamples ... 1000. A variation of the conjecture where x , y , z instead of A , B , C must have a common prime factor is not true. See, for example math 27 4 162 3 9 7 math . Beal s conjecture is a generalization ... a common factor, it can be divided out of each to yield an equation with smaller, coprime bases. The conjecture ... R. Daniel Mauldin title A Generalization of Fermat s Last Theorem The Beal Conjecture and Prize ... notices 199711 beal.pdf PlanetMath title Beal s Conjecture urlname BealsConjecture http mathoverflow.net questions 28764 status of beal tijdeman zagier conjecture DEFAULTSORT Beal s Conjecture Category ... more details
The Macdonald conjecture could be one of several conjectures due to harvtxt Macdonald 1982 Macdonald s conjectures about Macdonald polynomial s, Macdonald s generalization of the Dyson conjecture , Macdonald s generalization of the Mehta integral . References Citation authorlink Ian G. Macdonald last1 Macdonald first1 I. G. title Some conjectures for root systems doi 10.1137 0513070 id MathSciNet id 674768 year 1982 journal SIAM Journal on Mathematical Analysis issn 0036 1410 volume 13 issue 6 pages 988 1007 mathdab ... more details
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