A New Proof of the Garoufalidis-Le-Zeilberger Quantum MacMahon Master Theorem
英文摘要：
We propose a new proof of the quantum version of MacMahon's Master Theorem, established by Garoufalidis, Le and Zeilberger.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
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, Le 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.
math.COmath.QA
Koszul algebras and the quantum MacMahon Master Theorem
We give a new proof of the quantum version of MacMahon's Master Theorem due to Garoufalidis, Le and Zeilberger (one-parameter case) and to Konvalinka and Pak (multiparameter case) by deriving it from known facts about Koszul algebras.
math.COmath.QA
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 $β$-extension and Krattenthaler-Schlosser's $q$-analogue.
math.CO
A basis for the right quantum algebra and the "1=q" principle
We construct a basis for the right quantum algebra introduced by Garoufalidis, Le and Zeilberger and give a method making it possible to go from an algebra submitted to commutation relations (without the variable q) to the right quantum algebra by means of an appropriate weight-function. As a consequence, a strong quantum MacMahon Master Theorem is derived. Besides, the algebra of biwords is systematically in use.
math.COmath.QA
A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra
The right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A combinatorial proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester's determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by Foata. This paper makes explicit the connection between this transformation and right-quantum linear algebra identities; applications include a new combinatorial proof of the right-quantum matrix inverse…
math.CO
