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Double-dimer condensation and the PT-DT correspondence

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arxiv 2109.11773 v2 pith:CHEM4LFZ submitted 2021-09-24 math.CO math.AG

Helen Jenne , Gautam Webb , Benjamin Young This is my paper · ORCID
classification math.COmath.AG
keywords condensationdouble-dimergeneratingplanetheoryalgebraicapplicationbox-counting
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We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory) are equal up to a factor of MacMahon's generating function for plane partitions. The main tools in our proof are a Desnanot-Jacobi-type condensation identity, and a novel application of the tripartite double-dimer model of Kenyon-Wilson.

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  1. Bijectivizing the PT-DT Correspondence

    math.CO 2024-11 accept novelty 6.0 of 10

    New bijective proofs show that one-leg and two-leg skew plane partitions and reverse plane partitions have generating functions differing exactly by MacMahon's function.

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