The enumeration of maximally clustered permutations

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dc.creatorDenoncourt, Hugh
dc.creatorJones, Brant C.
dc.date2007-04-26
dc.date2008-09-25
dc.date.accessioned2026-07-07T10:04:45Z
dc.date.available2026-07-07T10:04:45Z
dc.descriptionThe maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and the fully-commutative permutations. In this work, we show that the generating functions for certain fully-commutative pattern classes can be transformed to give generating functions for the corresponding freely-braided and maximally clustered pattern classes. Moreover, this transformation of generating functions is rational. As a result, we obtain enumerative formulas for the pattern classes mentioned above as well as the corresponding hexagon-avoiding pattern classes where the hexagon-avoiding permutations are characterized by avoiding 46718235, 46781235, 56718234, and 56781234.
dc.description17 pages; corrected typos, added new section
dc.identifierhttps://arxiv.org/abs/0704.3469
dc.identifierhttp://arxiv.org/abs/0704.3469
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169792
dc.subjectCombinatorics
dc.subject05A15
dc.titleThe enumeration of maximally clustered permutations
dc.typetext

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