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Computing a pyramid partition generating function with dimer shuffling · Around

2007

Computing a pyramid partition generating function with dimer shuffling

Young, Benjamin

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We verify a recent conjecture of Kenyon/Szendroi, arXiv:0705.3419, by computing the generating function for pyramid partitions.

Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson--Thomas theory of a non-commutative resolution of the conifold singularity {x1x2 -x3x4 = 0}.
The proof does not require algebraic geometry; it uses a modified version of the domino shuffling algorithm of Elkies, Kuperberg, Larsen and Propp.

Built on

Alternating sign matrices and domino tilings ii
Noam Elkies, Greg Kuperberg, Michael Larsen, and James Propp · 1992
Earlier work this paper cites.
Talk at the workshop on random partitions and Calabi-Yau crystals, Amsterdam, 2005
Richard Kenyon · 2005
Earlier work this paper cites.

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Then

Non-commutative Donaldson-Thomas theory and the conifold
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Balázs Szendrői · 2007
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Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds, June 2008
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Ben Young, with an appendix by Jim Bryan · 2008
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