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 Garoufa-lidis, 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. R ´ ESUMÉ. Nousétudions certaines spécialisations et extensions de la version quantique du " Master Theorem " de MacMahon, ´ etabli par Garo-ufalidis, Lê et Zeilberger. En particulier, nous obtenons un (t, q)-analogue pour la version non-commutative de Cartier-Foata et un (t, q)-analogue semi-fort pour l'lagèbre contextuelle. 1. Introduction The Master Theorem derived by MacMahon [Ma15, vol. 1, p. 97] is a fundamental result in Combinatorial Analysis and has had many applications. To state it in a context relevant to its further noncommutative extensions we use the following notations. Let r be a positive integer and A the alphabet {1, 2,. .. , r}. A biword on A is a 2 × n matrix α = x 1 ···x n