arXiv math/06077372006-07-28math.CO

Non-commutative extensions of the MacMahon Master Theorem

Matjaz Konvalinka, Igor Pak

备注：: 28 pages, 6 figures

英文摘要：

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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