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We find rational expressions for all minors of the weighted path matrix of a directed graph, generalizing the classical Lindstrom/Gessel-Viennot result for acyclic directed graphs.
Coincidence probabilities
Samuel Karlin and James McGregor · 1959
Earlier work this paper cites.
On the vector representations of induced matroids
Bernt Lindström · 1973
Earlier work this paper cites.
Binomial determinants, paths, and hook length formulae
Ira Gessel and Gérard Viennot · 1985
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Heaps of pieces. I. Basic definitions and combinatorial lemmas
Gérard Xavier Viennot · 1989
Cited alongside, same era.
Lattice paths and determinants
Martin Aigner · 2001
Cited alongside, same era.
Loop-erased walks and total positivity
Sergey Fomin · 2001
Cited alongside, same era.
A formula for Plücker coordinates associated with a planar network
Kelli Talaska · 2008
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Trek separation for Gaussian graphical models
Seth Sullivant, Kelli Talaska, and Jan Draisma · 2010
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