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.
@article{10_37236_13789,
author = {Cruz Godar and Benjamin Young},
title = {Bijectivizing the {PT-DT} correspondence},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13789},
zbl = {1569.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13789/}
}
TY - JOUR
AU - Cruz Godar
AU - Benjamin Young
TI - Bijectivizing the PT-DT correspondence
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/13789/
DO - 10.37236/13789
ID - 10_37236_13789
ER -
%0 Journal Article
%A Cruz Godar
%A Benjamin Young
%T Bijectivizing the PT-DT correspondence
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/13789/
%R 10.37236/13789
%F 10_37236_13789
Cruz Godar; Benjamin Young. Bijectivizing the PT-DT correspondence. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13789
