Some statistics on restricted 132 involutions

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dc.creatorGuibert, O.
dc.creatorMansour, T.
dc.date2002-06-17
dc.date.accessioned2026-07-07T04:49:10Z
dc.date.available2026-07-07T04:49:10Z
dc.descriptionIn [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the number of inversions and rises of the involutions onto the words. This is the starting point for considering two different directions: even/odd involutions and statistics of some generalized patterns. Thus we first study generating functions for the number of even or odd involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern $τ$ on k letters. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. Next, we consider other statistics on 132-avoiding involutions by counting an occurrences of some generalized patterns, related to the enumeration according to the number of rises.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0206169
dc.identifierhttp://arxiv.org/abs/math/0206169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64323
dc.subjectCombinatorics
dc.titleSome statistics on restricted 132 involutions
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