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Kazhdan-Lusztig polynomials of thagomizer matroids. (English) Zbl 1369.05029
Summary: We introduce thagomizer matroids and compute the Kazhdan-Lusztig polynomial of a rank \(n+1\) thagomizer matroid by showing that the coefficient of \(t^k\) is equal to the number of Dyck paths of semilength \(n\) with \(k\) long ascents. We also give a conjecture for the \(S_n\)-equivariant Kazhdan-Lusztig polynomial of a thagomizer matroid.

05B35 Combinatorial aspects of matroids and geometric lattices
05A15 Exact enumeration problems, generating functions
20C30 Representations of finite symmetric groups
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
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