An extension of the Lindström-Gessel-Viennot theorem (Q2144326)

Summary: 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.