Lattice Walks in the Octant with Infinite Associated Groups

TL;DR

This paper investigates lattice walks confined to the positive octant with infinite associated groups, identifying only 12 such groups up to isomorphism and linking their structure to Hadamard models.

Contribution

It classifies all infinite groups associated with these lattice walk models and reveals a connection to Hadamard models, advancing understanding of their algebraic structure.

Findings

Only 12 infinite groups appear up to isomorphism

A connection between the group structure and Hadamard models is established

Provides a classification of models with infinite associated groups

Abstract

Continuing earlier investigations of restricted lattice walks in $\mathbb{N}^3$, we take a closer look at the models with infinite associated groups. We find that up to isomorphism, only 12 different infinite groups appear, and we establish a connection between the group of a model and the model being Hadamard.