Séminaire Lotharingien de Combinatoire, 85B.89 (2021), 12 pp.

Helen Jenne, Gautam Webb and Benjamin Young

The Combinatorial PT-DT Correspondence

Abstract. We resolve a 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.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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