Viewing Determinants as Nonintersecting Lattice Paths yields Classical Determinantal Identities Bijectively

  • Markus Fulmek
Keywords: determinantal identities, nonintersecting lattice paths, Schur function identities


In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindström-Gessel-Viennot-method and the Jacobi Trudi identity together with elementary observations.

After some preparations, this point of view provides "graphical proofs'' for classical determinantal identities like the Cauchy-Binet formula, Dodgson's condensation formula, the Plücker relations, Laplace's expansion and Turnbull's identity. Also, a determinantal identity generalizing Dodgson's condensation formula is presented, which might be new.

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