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

Matjaž Konvalinka
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Abstract

The 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.

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Matjaž Konvalinka. 2007-03-07. A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra. https://arxiv.org/abs/math/0703203

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