Viewing Determinants as Nonintersecting Lattice Paths yields Classical Determinantal Identities Bijectively

Abstract

In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindström–Gessel–Viennotmethod 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… (More)

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