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Tiered trees and Theta operators

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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].

Dates and versions

hal-03869254 , version 1 (24-11-2022)

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Michele d'Adderio, Alessandro Iraci, Yvan Le Borgne, Marino Romero, Anna Vanden Wyngaerd. Tiered trees and Theta operators. 2022. ⟨hal-03869254⟩

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