Enumerating coloured partitions in 2 and 3 dimensions
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.
Cite
@article{arxiv.1811.12857,
title = {Enumerating coloured partitions in 2 and 3 dimensions},
author = {Ben Davison and Jared Ongaro and Balazs Szendroi},
journal= {arXiv preprint arXiv:1811.12857},
year = {2020}
}
Comments
31 pages, 5 figures, minor corrections