Double series representations for Schur's partition function and related identities

George Andrews, Kathrin Bringmann, Karl Mahlburg

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We prove new double summation hypergeometric q-series representations for several families of partitions, including those that appear in the famous product identities of Göllnitz, Gordon, and Schur. We give several different proofs for our results, using bijective partitions mappings and modular diagrams, the theory of q-difference equations and recurrences, and the theories of summation and transformation for q-series. We also consider a general family of similar double series and highlight a number of other interesting special cases.

Original languageEnglish (US)
Pages (from-to)102-119
Number of pages18
JournalJournal of Combinatorial Theory. Series A
Volume132
DOIs
StatePublished - May 1 2015

Fingerprint

Q-series
Schur Functions
Series Representation
Difference equations
Partition Function
Summation
Partition
Q-difference Equations
Bijective
Recurrence
Diagram
Series
Family

All Science Journal Classification (ASJC) codes

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

Cite this

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Double series representations for Schur's partition function and related identities. / Andrews, George; Bringmann, Kathrin; Mahlburg, Karl.

In: Journal of Combinatorial Theory. Series A, Vol. 132, 01.05.2015, p. 102-119.

Research output: Contribution to journalArticle

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