Non-commutative extensions of the MacMahon Master Theorem
Abstract
We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to the β-extension and Krattenthaler-Schlosser's q-analogue.
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