On 3-dimensional Lattice Walks Confined to the Positive Octant

@inproceedings{Bostan2014On3L,
  title={On 3-dimensional Lattice Walks Confined to the Positive Octant},
  author={Alin Bostan and Mireille Bousquet-M{\'e}lou and Manuel Kauers and Stephen Melczer},
  year={2014}
}
Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in {0,±1}2: the generating function is D-finite if and only if a certain group associated with the step set is finite. We explore in this paper the analogous problem for 3-dimensional walks confined to the positive octant. The first difficulty is their number: we have to examine no less than 11 074 225 step sets in… CONTINUE READING