Non-commutative extensions of the MacMahon Master Theorem
arXiv:math/0607737
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.
28 pages, 6 figures