Year: 2025
Type: article
Abstract: Pandharipande-Thomas theory and Donaldson-Thomas theory (PT and DT) are two branches of enumerative geometry in which particular generating functions arise that count plane-partition-like objects. That these generating functions differ only by a factor of MacMahon's function was proven recursively by Jenne, Webb, and Young using the double dimer model. We bijectivize two special cases of the result by formulating these generating functions using vertex operators and applying a particular type of local involution known as a toggle, first introduced in the form we use by Pak.
DOI: 10.37236/13789
Authors: Cruz Godar, Benjamin Young
Institution: University of Oregon
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411450192