Enumerating coloured partitions in 2 and 3 dimensions

Ben Davison, Jared Ongaro, Balazs Szendroi

Research output: Contribution to journalArticlepeer-review


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
Issue number1
Early online date19 Jul 2019
Publication statusPublished - 30 Nov 2020


  • math.AG
  • hep-th
  • math.CO


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