An inverse matrix formula in the right-quantum algebra
The electronic journal of combinatorics, Tome 15 (2008)
The right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A bijective 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; we give a new, bijective proof of the right-quantum matrix inverse theorem, we show that similar techniques prove the right-quantum Jacobi ratio theorem, and we use the matrix inverse formula to find a generalization of the (right-quantum) MacMahon master theorem.
@article{10_37236_747,
author = {Matja\v{z} Konvalinka},
title = {An inverse matrix formula in the right-quantum algebra},
journal = {The electronic journal of combinatorics},
year = {2008},
volume = {15},
doi = {10.37236/747},
zbl = {1158.15302},
url = {http://geodesic.mathdoc.fr/articles/10.37236/747/}
}
Matjaž Konvalinka. An inverse matrix formula in the right-quantum algebra. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/747
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