An extension of the Lindström-Gessel-Viennot theorem

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.

24 pages, to appear in the Electronic Journal of Combinatorics

References in corpus (1)

• Enumeration of Domino Tilings of an Aztec Rectangle with boundary defects