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

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dc.creatorJones, Brant C.
dc.date2007-04-23
dc.date.accessioned2026-07-07T07:57:54Z
dc.date.available2026-07-07T07:57:54Z
dc.descriptionWe provide a non-recursive description for the bounded admissible sets of masks used by Deodhar's algorithm to calculate the Kazhdan--Lusztig polynomials $P_{x,w}(q)$ 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0704.3067
dc.identifierhttp://arxiv.org/abs/0704.3067
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127819
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject20C08
dc.titleKazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations
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