Partitions and Durfee Dissection

DOI10.2307/2373804zbMath0409.10006OpenAlexW2319538346MaRDI QIDQ4196476

George E. Andrews

Publication date: 1979

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2373804

zbMATH Keywords

PartitionsRogers-Ramanujan IdentitiesDurfee Squares

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Elementary theory of partitions (11P81) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (36)

Further 𝑞-series identities and conjectures relating false theta functions and characters ⋮ Durfee rectangles and the Jacobi triple product identity ⋮ Generalization of Dyson's rank and non-Rogers-Ramanujan partitions ⋮ Overpartition pairs ⋮ ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES ⋮ Congruences for partitions with odd parts distinct modulo 5 ⋮ Partition bijections, a survey ⋮ Ramanujan-type partial theta identities and conjugate Bailey pairs. II: Multisums ⋮ Group actions on partitions ⋮ Separable integer partition classes ⋮ On 3-regular partitions with odd parts distinct ⋮ New companions to Gordon identities from commutative algebra ⋮ Durfee rectangle identities via symmetric functions ⋮ New companions to the Andrews-Gordon identities motivated by commutative algebra ⋮ Anti-lecture Hall compositions and overpartitions ⋮ A three-way correspondence between partitions ⋮ An extension to overpartitions of the Rogers-Ramanujan identities for even moduli ⋮ Dyson's new symmetry and generalized Rogers-Ramanujan identities ⋮ Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras ⋮ Overpartition pairs and two classes of basic hypergeometric series ⋮ New congruences modulo 5 and 9 for partitions with odd parts distinct ⋮ Partition identities involving gaps and weights ⋮ Parity considerations in Andrews-Gordon identities ⋮ A proof of Bressoud's conjecture related to the Rogers-Ramanujan identities ⋮ A combinatorial proof of the Rogers--Ramanujan and Schur identities ⋮ Arithmetic properties of partitions with odd parts distinct ⋮ Hall-Littlewood Functions, Plane Partitions, and the Rogers-Ramanujan Identities ⋮ Overpartitions ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Marking and shifting a part in partitions ⋮ Generalized Rogers-Ramanujan bijections ⋮ Combinatorial interpretations for identities using chromatic partitions ⋮ CONGRUENCE PROPERTIES MODULO 5 AND 7 FOR THE pod FUNCTION ⋮ Principal subspaces for the affine Lie algebras in types \(D, E\) and \(F\) ⋮ Generalizations of Dyson’s rank on overpartitions ⋮ Some observations on Dyson's new symmetries of partitions

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