Constant term solution for an arbitrary number of osculating lattice paths

TL;DR

This paper derives a constant term formula for counting osculating lattice paths, which are directed paths that can touch but not cross or share edges, by solving related difference equations.

Contribution

It introduces a novel constant term formula for enumerating osculating lattice paths, expanding combinatorial enumeration methods.

Findings

Provides a closed-form constant term expression for osculating paths

Solves a set of difference equations to obtain enumeration formula

Enhances understanding of lattice path combinatorics

Abstract

Osculating paths are sets of directed lattice paths which are not allowed to cross each other or have common edges, but are allowed to have common vertices. In this work we derive a constant term formula for the number of such lattice paths by solving a set of simultaneous difference equations.