A New Proof of the Garoufalidis-Lê-Zeilberger Quantum MacMahon Master Theorem
نویسندگان
چکیده
We propose a new proof of the quantum version of MacMahon’s Master Theorem, established by Garoufalidis, Lê and Zeilberger. RÉSUMÉ. Nous proposons une nouvelle démonstration de la version quantique du Master Théorème de MacMahon, établi par Garoufalidis, Lê et Zeilberger.
منابع مشابه
An Inverse Matrix Formula in 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 bijective 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 Foat...
متن کاملA 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 ...
متن کاملThe quantum MacMahon Master Theorem.
We state and prove a quantum generalization of MacMahon's celebrated Master Theorem and relate it to a quantum generalization of the boson-fermion correspondence of physics.
متن کاملSpecializations and Extensions of the quantum
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.
متن کاملNon-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-LêZeilberger. 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. Introduction The MacMahon Master Theorem is one of the jewels in enumerative combinatori...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005