Infinite Orders and Non-$D$-finite Property of $3$-Dimensional Lattice Walks

Daniel K. Du, Qing-Hu Hou, Rong-Hua Wang

Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant ${\mathbb{N}}^3$. For the $35548$ non-trivial models with at most six steps, they…