Non-commutative extensions of the MacMahon Master Theorem
  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. 
Matjaz Konvalinka, Igor Pak