Tiered trees and Theta operators
Combinatorics
2023-03-02 v1
Abstract
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers, and torus orbits on certain homogeneous varieties. In this paper, we use Theta operators, introduced in [D'Adderio-Iraci-VandenWyngaerd-Theta-2021], to give a symmetric function formula that enumerates these trees. We then formulate a general conjecture that extends this result, a special case of which might give some insight about how to formulate a unified Delta conjecture [Haglund-Remmel-Wilson-2018].
Cite
@article{arxiv.2202.05706,
title = {Tiered trees and Theta operators},
author = {Michele D'Adderio and Alessandro Iraci and Yvan LeBorgne and Marino Romero and Anna Vanden Wyngaerd},
journal= {arXiv preprint arXiv:2202.05706},
year = {2023}
}