# Linear recurrences for cylindrical networks

## TL;DR

This paper establishes a general linear recurrence theorem for tuples of paths in cylindrical networks, extending classical path enumeration results to a cylindrical setting and applying it to various combinatorial objects.

## Contribution

It introduces a cylindrical analog of the Lindström-Gessel-Viennot theorem, broadening the scope of path enumeration techniques in combinatorics.

## Key findings

- Proves a general linear recurrence for cylindrical network paths
- Applies the theorem to Schur functions, plane partitions, and domino tilings
- Extends classical path enumeration results to cylindrical geometries

## 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 Lindstr\"om-Gessel-Viennot theorem. We illustrate the result by applying it to Schur functions, plane partitions, and domino tilings.