On the distance between the expressions of a permutation

dc.creatorAutord, Marc
dc.creatorDehornoy, Patrick
dc.date2009-02-18
dc.date.accessioned2026-07-07T12:43:29Z
dc.date.available2026-07-07T12:43:29Z
dc.descriptionWe prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n^4), a sharp bound. Using a connection with the intersection numbers of certain curves in van Kampen diagrams, we prove that this bound is sharp, and give a practical criterion for proving that the derivations provided by the reversing algorithm of [Dehornoy, JPAA 116 (1997) 115-197] are optimal. We also show the existence of length l expressions whose reversing requires C l^4 elementary steps.
dc.identifierhttps://arxiv.org/abs/0902.3074
dc.identifierhttp://arxiv.org/abs/0902.3074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220438
dc.subjectCombinatorics
dc.subject20B30, 05E15, 20F55, 20F36
dc.titleOn the distance between the expressions of a permutation
dc.typetext

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