Linear Recurrences for Cylindrical Networks

Abstract

We prove a general theorem that gives a linear recurrence for tuples of paths in every cylindrical network. This can be seen as a cylindrical analog of the Lindström-Gessel-Viennot theorem. We illustrate the result by applying it to Schur functions, plane partitions, and domino tilings.• alternating sign matrices (equivalently, totally symmetric selfcomplementary plane partitions) [3,29],