Enumerating coloured partitions in 2 and 3 dimensions

Ben Davison, Jared Ongaro, Balazs Szendroi

Research output: Contribution to journalArticlepeer-review

Abstract

We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a conjecture concerning a factorisation property of the generating function of coloured plane partitions that can be thought of as an orbifold analogue of a conjecture of Maulik et al., now a theorem, in three-dimensional Donaldson-Thomas theory. We study natural quantisations of the generating functions arising from geometry, discuss a quantised version of our conjecture, and prove a positivity result for the quantised coloured plane partition function under a geometric assumption.
Original languageEnglish
Pages (from-to) 479 - 505
Number of pages27
JournalMathematical Proceedings of The Cambridge Philosophical Society
Volume183
Issue number1
Early online date19 Jul 2019
DOIs
Publication statusPublished - 30 Nov 2020

Keywords

  • math.AG
  • hep-th
  • math.CO

Fingerprint

Dive into the research topics of 'Enumerating coloured partitions in 2 and 3 dimensions'. Together they form a unique fingerprint.

Cite this