Walks in the quarter plane with multiple steps. (English. French summary) Zbl 1335.05012
Proceedings of the 27th international conference on formal power series and algebraic combinatorics, FPSAC 2015, Daejeon, South Korea, July 6–10, 2015. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 25-36 (2015).
Summary: We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. These families cover all the models with multiplicites 0, 1, 2, or 3, which were experimentally found to be D-finite – with three noteworthy exceptions.
For the entire collection see [Zbl 1333.05004].
For the entire collection see [Zbl 1333.05004].
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
