Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectively
Combinatorics
2010-10-20 v1
Abstract
In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindstr\"om-Gessel-Viennot interpretation of semistandard Young tableaux and the Jacobi-Trudi identity together with elementary observations. After some preparations, this point of view provides very simple "graphical proofs" for classical determinantal identities like the Cauchy--Binet formula, Dodgson's condensation formula, the Pl\"ucker relations and Laplace's expansion. Also, a determinantal identity generalizing Dodgson's condensation formula is presented, which might be new.
Keywords
Cite
@article{arxiv.1010.3860,
title = {Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectively},
author = {Markus Fulmek},
journal= {arXiv preprint arXiv:1010.3860},
year = {2010}
}