Partition identities and quiver representations

Richárd Rimányi, Anna Weigandt, Alexander Yong

Research output: Contribution to journalArticlepeer-review

Abstract

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke’s identity in the case of quivers Q of Dynkin type A. Our identity is stated in terms of the lacing diagrams of S. Abeasis–A. Del Fra, which parameterize orbits of the representation space of Q for a fixed dimension vector..

Original languageEnglish (US)
Pages (from-to)129-169
Number of pages41
JournalJournal of Algebraic Combinatorics
Volume47
Issue number1
DOIs
StatePublished - Feb 1 2018

Keywords

  • Durfee square
  • Multipartitions
  • Quiver representations

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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