Non-commutative Sylvester's determinantal identity

2007/03/08 by Matjaž Konvalinka, Matjaz Konvalinka, Konvalinka, Matjaz · 1 citation
Mathematics · #05A30 #15A15 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A30 #msc:15A15

paper · pdf · doi:10.48550/arxiv.math/0703213

28 pages, 8 figures

arxiv created 2007/03/08 · openalex publication_date 2007/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• An algebraic extension of the MacMahon Master Theorem

Cited by

• N-homogeneous superalgebras

Related

• Generalizations of Sylvester's determinantal identity
• On an identity of Sylvester
• Yet Another Proof of Sylvester's Determinant Identity
• A new family of polynomial identities for computing determinants
• An Elementary Proof of Sylvester's Double Sums for Subresultants