Computing a pyramid partition generating function with dimer shuffling
Combinatorics
2008-07-03 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0709.3079,
title = {Computing a pyramid partition generating function with dimer shuffling},
author = {Benjamin Young},
journal= {arXiv preprint arXiv:0709.3079},
year = {2008}
}
Comments
19 pages, 13 figures. v2: fixed minor typos, updated references and future work; added some definitions to Section 6