Non-commutative Sylvester's determinantal identity

Abstract

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 $\beta$-extension that is both a generalization of Sylvester's identity and the $\beta$-extension of the MacMahon master theorem.

28 pages, 8 figures

References in corpus (1)

• A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra

Cited by in corpus (2)

• A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra
• N-homogeneous superalgebras