Séminaire Lotharingien de Combinatoire, 93B.39 (2025), 12 pp.

Tatyana Benko and Benjamin Young

Double Boxes and Double Dimers

Abstract. We give a combinatorial proof of a result in rank 2 Donaldson-Thomas theory, which states that the generating function for certain plane-partition-like objects, called double-box configurations, is equal to a product of MacMahon's generating function for (boxed) plane partitions. In our proof, we first give the correspondence between double-box configurations and double-dimer configurations on the hexagon lattice with a particular tripartite node pairing. Using this correspondence, we apply graphical condensation and double-dimer condensation to prove the result.

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

The following versions are available:

PDF (793 K)
TeX version