88304am永利集团

For each integer $n\ge 1$, the thagomizer matroid is the graphic matroid of the complete tripartite graph $K_{1,1,n}$ (with parts of sizes $1,1,n$); for $n\ge 2$, its full automorphism group is the hyperoctahedral group. We compute the Kazhdan--Lusztig polynomial and the inverse Kazhdan--Lusztig polynomial in the equivariant setting for this action, and we show that each coefficient is an honest representation with a multiplicity-free irreducible decomposition. Taking dimensions recovers the previously known nonequivariant thagomizer polynomials, and the coefficient formulas are naturally stated using the wreath product Frobenius characteristic for the hyperoctahedral group.

张彪，主要从事组合数学中单峰型理论和对称函数理论的研究工作。2015年6月博士毕业于南开大学，2018年8月至2019年8月到美国宾夕法尼亚大学访问。在《J.Comb.Theory Ser. A》、《Adv. Appl. Math.》、《SIAM J. Discrete Math.》、《Bull. Lond. Math. Soc.》、《Proc. Amer. Math. Soc.》等期刊发表学术论文三十余篇，主持国家自然科学基金3项、天津市自然科学基金1项。