A. Pun

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math.CO2025

The nonsymmetric shuffle theorem

Jonah Blasiak, Mark Haiman, Jennifer Morse +2

The shuffle conjecture of Haglund et al. expresses the symmetric function $\nabla e_{n}$ as a sum over labeled Dyck paths. Here $\nabla$ is an operator on symmetric functions defined…

math.CO2025

Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials

Jonah Blasiak, Mark Haiman, Jennifer Morse +2

The plethystic transformation $f [X] \mapsto f [X / (1 - t)]$ and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsy…

math.CO2024

On the Correspondence Between Integer Sequences and Vacillating Tableaux

Zhanar Berikkyzy, Pamela E. Harris, Anna Pun +2

A fundamental identity in the representation theory of the partition algebra is $n^{k} = \sum_{I^} » f^{I^} » m_{k}^{I^} »$ for $n \geq 2 k$ , where $I^»$ ranges over integer partitions of $n$ , $f^{I^} »$ …