English

Non-commutative Sylvester's determinantal identity

Combinatorics 2007-05-23 v1

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

Cite

@article{arxiv.math/0703213,
  title  = {Non-commutative Sylvester's determinantal identity},
  author = {Matjaz Konvalinka},
  journal= {arXiv preprint arXiv:math/0703213},
  year   = {2007}
}

Comments

28 pages, 8 figures