Geodesic
Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectively
Markus Fulmek1
1Fakultät für Mathematik Universität Wien
The electronic journal of combinatorics, Tome 19 (2012) no. 3

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Zbl arXiv
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.
DOI : 10.37236/2530
Classification : 05A19, 05E05
Mots-clés : determinantal identities, nonintersecting lattice paths, Schur function identities

Markus Fulmek  1

1 Fakultät für Mathematik Universität Wien 
Markus Fulmek. Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectively. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2530
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     title = {Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectively},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
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     doi = {10.37236/2530},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/2530/}
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