Computing a pyramid partition generating function with dimer shuffling

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Abstract

We verify a recent conjecture of Kenyon/Szendro{combining double acute accent}i 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 {x1 x2 - x3 x4 = 0} ⊂ C4. The proof does not require algebraic geometry; it uses a modified version of the domino shuffling algorithm of Elkies, Kuperberg, Larsen and Propp [Noam Elkies, Greg Kuperberg, Michael Larsen, James Propp, Alternating sign matrices and domino tilings. II, J. Algebraic Combin. 1 (3) (1992) 219-234]. © 2008 Elsevier Inc. All rights reserved.

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APA

Young, B. (2009). Computing a pyramid partition generating function with dimer shuffling. Journal of Combinatorial Theory. Series A, 116(2), 334–350. https://doi.org/10.1016/j.jcta.2008.06.006

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