Geodesic
An extension of the Lindström-Gessel-Viennot theorem
Yi-Lin Lee1
1Indiana University at Bloomington
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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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.
DOI : 10.37236/10913
Classification : 05C22, 05C20, 05C62, 05A15, 05C30, 05C38
Mots-clés : weighted directed acyclic graph

Yi-Lin Lee  1

1 Indiana University at Bloomington 
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     author = {Yi-Lin Lee},
     title = {An extension of the {Lindstr\"om-Gessel-Viennot} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/10913},
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Yi-Lin Lee. An extension of the Lindström-Gessel-Viennot theorem. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10913

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