Computing a pyramid partition generating function with dimer shuffling

2007/09/19 by Benjamin Young, Young, Benjamin · 4 citations
Mathematics · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AG #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.0709.3079

19 pages, 13 figures. v2: fixed minor typos, updated references and future work; added some definitions to Section 6

openalex publication_date 2007/09/19 · arxiv created 2008/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Wall crossing in local Calabi Yau manifolds
• Invariance of orientation data for ind-constructible Calabi-Yau A_∞ categories under derived equivalence
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Open BPS wall crossing and M-theory

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