Restricted involutions and Motzkin paths

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dc.creatorBarnabei, M.
dc.creatorBonetti, F.
dc.creatorSilimbani, M.
dc.date2008-12-02
dc.date2008-12-17
dc.date.accessioned2026-07-07T12:13:18Z
dc.date.available2026-07-07T12:13:18Z
dc.descriptionWe show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321 and 3412. As a consequence, we derive characterizations of Motzkin paths corresponding to involutions avoiding either 4321 or 3412 together with any pattern of length 3. Furthermore, we exploit the described bijection to study some notable subsets of the set of restricted involutions, namely, fixed point free and centrosymmetric restricted involutions.
dc.description22 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/0812.0463
dc.identifierhttp://arxiv.org/abs/0812.0463
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210800
dc.subjectCombinatorics
dc.subject05E15; 05A15; 20B35
dc.titleRestricted involutions and Motzkin paths
dc.typetext

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