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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.arXiv:1610.05349v2 fatcat:c2kimkpenjb6zn53qkcyq3bpwi