A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra
Abstract
The right-quantum algebra was introduced recently by Garoufalidis, L\^e 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.
Keywords
Cite
@article{arxiv.math/0703203,
title = {A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra},
author = {Matjaž Konvalinka},
journal= {arXiv preprint arXiv:math/0703203},
year = {2007}
}
Comments
17 pages, 8 figures