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math.CO2025
Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
Alice L. L. Gao, Yun Li, Matthew H. Y. Xie
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…
math.CO2025
The inverse -polynomial of a matroid
Alice L. L. Gao, Xuan Ruan, Matthew H. Y. Xie
Motivated by the -polynomials of matroids, Ferroni, Matherne, Stevens, and Vecchi introduced the inverse -polynomial of a matroid. In this paper, we prove several fundamental…
math.CO2025
Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids
Matthew H. Y. Xie, Philip B. Zhang
Gao and Xie (2021) conjectured that the inverse Kazhdan-Lusztig polynomial of any matroid is log-concave. Although the inverse Kazhdan-Lusztig polynomial may not always have only r…