A Survey of Multipartitions Congruences and Identities

DOI10.1007/978-0-387-78510-3_1zbMath1183.11063OpenAlexW139756262MaRDI QIDQ3401681

George E. Andrews

Publication date: 1 February 2010

Published in: Surveys in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-78510-3_1

zbMATH Keywords

Partitionsmultipartitionspartition congruencestripentagonal number theorem

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Related Items (25)

Restricted \(k\)-color partitions ⋮ Infinite families of crank functions, Stanton-type conjectures, and unimodality ⋮ Some congruences for 3-component multipartitions ⋮ A weighted partition function connected to the Rogers-Szegő polynomials ⋮ Congruences modulo prime for fractional colour partition function ⋮ Message authentication based on cryptographically secure CRC without polynomial irreducibility test ⋮ Extension of a proof of the Ramanujan congruences for multipartitions ⋮ Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 ⋮ A theory of theta functions to the quintic base ⋮ Fractional powers of the generating function for the partition function ⋮ Approximations of analytic functions via generalized power product expansions ⋮ Infinite families of congruences modulo 7 for Ramanujan's general partition function ⋮ Congruences modulo powers of 5 for \(k\)-colored partitions ⋮ Principal series for general linear groups over finite commutative rings ⋮ Congruences for powers of the partition function ⋮ Congruences of multipartition functions modulo powers of primes ⋮ Parity considerations in Andrews-Gordon identities ⋮ Weighted generalized crank moments for \(k\)-colored partitions and Andrews-Beck type congruences ⋮ Unnamed Item ⋮ Some inequalities for Garvan's bicrank function of 2-colored partitions ⋮ Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra ⋮ THE TRI-PENTAGONAL NUMBER THEOREM AND RELATED IDENTITIES ⋮ Restricted k-color partitions, II ⋮ Multiranks and classical theta functions ⋮ The Littlewood-Richardson rule for wreath products with symmetric groups and the quiver of the categoryF≀FI_n

Cites Work

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• Multiple series Rogers-Ramanujan type identities
• Weights of multipartitions and representations of Ariki-Koike algebras.
• Ramanujan's method in \(q\)-series congruences
• Umbral calculus, Bailey chains, and pentagonal number theorems
• Multirestricted and rowed partitions
• THE TRI-PENTAGONAL NUMBER THEOREM AND RELATED IDENTITIES
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
• Partition congruences and the Andrews-Garvan-Dyson crank
• Proof of a conjecture of Ramanujan
• Ramanujan Congruences for p_-k(n)
• Further Identities of the Rogers-Ramanujan Type
• On identities of the Rogers-Ramanujan type

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