Two Dimensional Directed Lattice Walks with Boundaries

TL;DR

This paper introduces algorithms for analyzing constrained two-dimensional directed lattice walks, enabling calculations of various properties, with implementations in Maple, and revisits previous results as a special case.

Contribution

It provides a general algorithmic framework for studying 2D directed lattice walks with boundaries, extending prior specific results.

Findings

Algorithms implemented in Maple for lattice walk calculations

Re-derivation of earlier results as a special case

Framework applicable to general step sets on square lattice

Abstract

We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two dimensions. As a special case, we rederive results of earlier works.