Weighted cylindric partitions

Walter Bridges, Ali K. Uncu

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

Abstract

Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include very general product-sides coming from work of Han and Xiong. In doing so, we are led to consider structures such as weighted cylindric partitions, symmetric cylindric partitions and weighted skew double-shifted plane partitions. We prove some new identities and obtain new proofs of known identities, including the Göllnitz–Gordon and Little Göllnitz identities as well as some beautiful Schmidt-type identities of Andrews and Paule.

Original languageEnglish
Pages (from-to)1309-1337
Number of pages29
JournalJournal of Algebraic Combinatorics
Volume56
Issue number4
Early online date26 Aug 2022
DOIs
Publication statusPublished - Dec 2022

Bibliographical note

Research of the first author is partially supported by the DFG (Project Number 281071066 TRR 191). Research of the second author is partly supported by EPSRC Grant Number EP/T015713/1 and partly by FWF Grant P-34501N.

Funding Information:
We would like to thank Krishnaswami Alladi, George E. Andrews, Jehanne Dousse, Guoniu Han, Ralf Hemmecke, and Peter Paule for their interest and encouragement. We would like to particularly thank Alexander Berkovich, Christian Krattencthaler, Ole Warnaar, and Wadim Zudilin for the discussion and their valuable feedback. We would also like to thank the anonymous referees for their careful reading and suggestions. The first author is partially supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics,” funded by the DFG (Project number 281071066 TRR 191). Research of the second author is partly supported by EPSRC Grant number EP/T015713/1 and partly by FWF Grant P-34501N.

Funding Information:
We would like to thank Krishnaswami Alladi, George E. Andrews, Jehanne Dousse, Guoniu Han, Ralf Hemmecke, and Peter Paule for their interest and encouragement. We would like to particularly thank Alexander Berkovich, Christian Krattencthaler, Ole Warnaar, and Wadim Zudilin for the discussion and their valuable feedback. We would also like to thank the anonymous referees for their careful reading and suggestions. The first author is partially supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics,” funded by the DFG (Project number 281071066 TRR 191). Research of the second author is partly supported by EPSRC Grant number EP/T015713/1 and partly by FWF Grant P-34501N.

Funding Information:
Research of the first author is partially supported by the DFG (Project Number 281071066 TRR 191). Research of the second author is partly supported by EPSRC Grant Number EP/T015713/1 and partly by FWF Grant P-34501N.

Publisher Copyright:
© 2022, The Author(s).

Keywords

  • Cylindric partitions
  • Partition diamonds
  • Partition identities
  • Skew double-shifted plane partitions
  • Weighted partition identities

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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