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arXiv · 2112.06115

An extension of the Lindström-Gessel-Viennot theorem

Yi-Lin Lee
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Abstract

Consider a weighted directed acyclic graph $G$ having an upward planar drawing. We give a formula for the total weight of the families of non-intersecting paths on $G$ with any given starting and ending points. While the Lindström-Gessel-Viennot theorem gives the signed enumeration of these weights (according to the connection type), our result provides the straight count, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points.

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Yi-Lin Lee. 2022-05-14. An extension of the Lindström-Gessel-Viennot theorem. https://doi.org/10.37236/10913

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