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arXiv · 2202.05706

Tiered trees and Theta operators

Michele D'Adderio·Alessandro Iraci·Yvan LeBorgne·Marino Romero·Anna Vanden Wyngaerd
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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].

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Michele D'Adderio, Alessandro Iraci, Yvan LeBorgne, Marino Romero, Anna Vanden Wyngaerd. 2022-02-11. Tiered trees and Theta operators. https://doi.org/10.1093/imrn%2Frnac258

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