An Algebraic Extension of the Macmahon Master Theorem
نویسنده
چکیده
We present a new algebraic extension of the classical MacMahon Master Theorem. The basis of our extension is the Koszul duality for non-quadratic algebras defined by Berger. Combinatorial implications are also discussed.
منابع مشابه
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-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 کاملNon-commutative Sylvester’s determinantal identity, preprint
Sylvester's identity is a classical determinantal identity with a straightforward linear algebra proof. We present a new, combinatorial proof of the identity, prove several non-commutative versions, and find a β-extension that is both a generalization of Sylvester's identity and the β-extension of the MacMahon master theorem.
متن کاملNon-Commutative Sylvester's Determinantal Identity
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a β-extension that is both a generalization of Sylvester’s identity and the β-extension of the quantum MacMahon master theorem.
متن کاملA New Proof of the Garoufalidis-Lê-Zeilberger Quantum MacMahon Master Theorem
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.
متن کاملSome generalizations of the MacMahon Master Theorem
We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.
متن کامل