# Automated positive part extraction for lattice path generating functions in the octant

## TL;DR

This paper proves that a specific class of three-dimensional lattice walks confined to the octant have D-finite generating functions, advancing the understanding of their algebraic nature using multivariate Laurent series.

## Contribution

It introduces a novel application of multivariate Laurent series theory to establish D-finiteness for certain octant lattice walk generating functions.

## Key findings

- Certain octant walks have D-finite generating functions
- Application of multivariate Laurent series in lattice path analysis
- Advances classification of lattice walk generating functions

## Abstract

The question of classifying the nature of the generating functions of restricted lattice walks has enjoyed much attention in past years. We prove that a certain class of octant walks have a D-finite generating function using the theory of multivariate formal Laurent series.