Specializations and extensions of the quantum MacMahon Master Theorem

We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Lê and Zeilberger. In particular, we obtain a (t,q)-analogue for the Cartier–Foata noncommutative version and a semi-strong (t,q)-analogue for the contextual algebra.