Partitions with part difference conditions and Bressoud's conjecture

Sun Kim, Ae Ja Yee

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

By employing Andrews' generalization of Watson's q-analogue of Whipple's theorem, Bressoud obtained an analytic identity, which specializes to most of the well-known theorems on partitions with part congruence conditions and difference conditions including the Rogers-Ramanujan identities. This led him to define two partition functions A and B depending on multiple parameters as combinatorial counterparts of his identity. Bressoud then proved that A = B for some very restricted choice of parameters and conjectured the equality to hold in full generality. We provide a proof of the conjecture for a much larger class of parameters, settling many cases of Bressoud's conjecture.

Original languageEnglish (US)
Pages (from-to)35-69
Number of pages35
JournalJournal of Combinatorial Theory. Series A
Volume126
Issue number1
DOIs
StatePublished - Jan 1 2014

Fingerprint

Partition
Rogers-Ramanujan Identities
Q-analogue
Theorem
Partition Function
Congruence
Equality
Class
Generalization

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

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abstract = "By employing Andrews' generalization of Watson's q-analogue of Whipple's theorem, Bressoud obtained an analytic identity, which specializes to most of the well-known theorems on partitions with part congruence conditions and difference conditions including the Rogers-Ramanujan identities. This led him to define two partition functions A and B depending on multiple parameters as combinatorial counterparts of his identity. Bressoud then proved that A = B for some very restricted choice of parameters and conjectured the equality to hold in full generality. We provide a proof of the conjecture for a much larger class of parameters, settling many cases of Bressoud's conjecture.",
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Partitions with part difference conditions and Bressoud's conjecture. / Kim, Sun; Yee, Ae Ja.

In: Journal of Combinatorial Theory. Series A, Vol. 126, No. 1, 01.01.2014, p. 35-69.

Research output: Contribution to journalArticle

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