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 $\beta$-extension and Krattenthaler-Schlosser's $q$-analogue.

28 pages, 6 figures

Cited by in corpus (1)

• An algebraic extension of the MacMahon Master Theorem