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Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
Alice L. L. Gao, Yun Li, Matthew H. Y. Xie
https://arxiv.org/abs/2510.11322 https://

Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
In this paper, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite graphs $K_{1,1,n}$. These polynomials were introduced by Proudfoot as an extension of the Kazhdan--Lusztig theory for matroids. We derive closed-form expressions for the $\mathfrak{S}_n$-equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids and present them explicitly in terms of the irreducible rep…