Enumerating coloured partitions in 2 and 3 dimensions
2019 ◽
Vol 169
(3)
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pp. 479-505
Keyword(s):
AbstractWe 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 basic 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.
1980 ◽
Vol 22
(3)
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pp. 439-455
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Keyword(s):
2001 ◽
Vol 131
(3)
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pp. 445-457
2009 ◽
Vol 213
(9)
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pp. 1665-1680
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2016 ◽
Vol 15
(04)
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pp. 1650062