Kazhdan–Lusztig polynomials for maximally-clustered hexagon-avoiding permutations

We provide a nonrecursive description for the bounded admissible sets of masks used by Deodhar's algorithm to calculate the Kazhdan–Lusztig polynomials Px,w(q) of type A, in the case when w is hexagon avoiding and maximally clustered. This yields a combinatorial description of the Kazhdan–Lusztig basis elements of the Hecke algebra associated to such permutations w. The maximally-clustered hexagon-avoiding elements are characterized by avoiding the seven classical permutation patterns {3421,4312,4321,46718235,46781235,56718234,56781234}. We also briefly discuss the application of heaps to permutation pattern characterization.