A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra

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dc.creatorKonvalinka, Matjaž
dc.date2007-03-07
dc.date.accessioned2026-07-07T07:50:40Z
dc.date.available2026-07-07T07:50:40Z
dc.descriptionThe right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A combinatorial proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester's determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by Foata. This paper makes explicit the connection between this transformation and right-quantum linear algebra identities; applications include a new combinatorial proof of the right-quantum matrix inverse theorem, and two new results, the right-quantum Jacobi ratio theorem and a generalization of the right-quantum MacMahon master thorem.
dc.description17 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math/0703203
dc.identifierhttp://arxiv.org/abs/math/0703203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125240
dc.subjectCombinatorics
dc.subject15A09, 05A15
dc.titleA generalization of Foata's fundamental transformation and its applications to the right-quantum algebra
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