Non-commutative extensions of the MacMahon master theorem

The MacMahon master theorem is a classic theorem in enumerative combinatorics with many interesting applications. Recently, a q-right-quantum generalization was given by Garoufalidis, Le, and Zeilberger. In this talk, we present a framework that not only gives a simple new proof of the classical result, but also generalizes the GLZ master theorem and gives some other extensions and applications.