# Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids

## TL;DR

This paper introduces a new formula for equivariant Kazhdan-Lusztig polynomials of thagomizer matroids, confirming a previous conjecture and linking to uniform matroids, advancing understanding in algebraic combinatorics.

## Contribution

The paper derives a new formula for these polynomials and confirms Gedeon's conjecture using the Pieri rule, connecting different classes of matroids.

## Key findings

- New formula for equivariant Kazhdan-Lusztig polynomials of thagomizer matroids
- Confirmation of Gedeon's conjecture using the Pieri rule
- Relation established between thagomizer and uniform matroids

## Abstract

The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig polynomials of thagomizer matroids with an action of symmetric groups. In this paper, we discover a new formula for these polynomials which is related to the equivariant Kazhdan-Lusztig polynomials of uniform matroids. Based on our new formula, we confirm Gedeon's conjecture by the Pieri rule.