Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids

Matthew H. Y. Xie; Philip B. Zhang

Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids

Combinatorics 2019-02-05 v1

Authors: Matthew H. Y. Xie , Philip B. Zhang

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.

Keywords

equivariant kazhdan-lusztig polynomial thagomizer matroid uniform matroid symmetric group action pieri rule

Cite

@article{arxiv.1902.01241,
  title  = {Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids},
  author = {Matthew H. Y. Xie and Philip B. Zhang},
  journal= {arXiv preprint arXiv:1902.01241},
  year   = {2019}
}

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10 pages

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