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{\bf Matja\v z Konvalinka}
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{\bf An Inverse Matrix Formula in the Right-Quantum Algebra}
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The right-quantum algebra was introduced recently by Garoufalidis,
L\^e 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.

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