Forest Polynomials and Pattern Avoidance

Fuente: arXiv
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Main Authors: Guo, Annie, Woodruff, Dora
Format: Preprint
Published: 2026
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author Guo, Annie
Woodruff, Dora
author_facet Guo, Annie
Woodruff, Dora
contents Forest polynomials, recently introduced by Nadeau and Tewari, can be thought of as a quasisymmetric analogue for Schubert polynomials. They have already been shown to exhibit interesting interactions with Schubert polynomials; for example, Schubert polynomials decompose positively into forest polynomials. We further describe this relationship by showing that a Schubert polynomial $\mathfrak{S}_w$ is a forest polynomial exactly when $w$ avoids a set of $6$ patterns. This result adds to the long list of properties of Schubert polynomials that are controlled by pattern avoidance.
format Preprint
id arxiv_https___arxiv_org_abs_2602_04036
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Forest Polynomials and Pattern Avoidance
Guo, Annie
Woodruff, Dora
Combinatorics
Forest polynomials, recently introduced by Nadeau and Tewari, can be thought of as a quasisymmetric analogue for Schubert polynomials. They have already been shown to exhibit interesting interactions with Schubert polynomials; for example, Schubert polynomials decompose positively into forest polynomials. We further describe this relationship by showing that a Schubert polynomial $\mathfrak{S}_w$ is a forest polynomial exactly when $w$ avoids a set of $6$ patterns. This result adds to the long list of properties of Schubert polynomials that are controlled by pattern avoidance.
title Forest Polynomials and Pattern Avoidance
topic Combinatorics
url https://arxiv.org/abs/2602.04036