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arXiv · 1811.12857

Enumerating coloured partitions in 2 and 3 dimensions

Ben Davison·Jared Ongaro·Balazs Szendroi
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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.

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Ben Davison, Jared Ongaro, Balazs Szendroi. 2018-11-30. Enumerating coloured partitions in 2 and 3 dimensions. https://doi.org/10.1017/s0305004119000252

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