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Non-commutative extensions of the MacMahon Master Theorem

Matjaz Konvalinka·Igor Pak
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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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Matjaz Konvalinka, Igor Pak. 2006-07-28. Non-commutative extensions of the MacMahon Master Theorem. https://arxiv.org/abs/math/0607737

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