Differential algebraic generating series of weighted walks in the quarter plane
arXiv:2104.05505
Abstract
In the present paper we study the nature of the trivariate generating series of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we complete the proof of the following theorem. The series satisfies a nontrivial algebraic differential equation in one of its variable, if and only if it satisfies a nontrivial algebraic differential equation in each of its variables.
References in corpus (7)
- Two Non-holonomic Lattice Walks in the Quarter Plane
- Intervals in the greedy Tamari posets
- Counting quadrant walks via Tutte's invariant method
- Walks in the quarter plane, genus zero case
- Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group
- Length derivative of the generating series of walks confined in the quarter plane
- On the Kernel curves associated with walks in the quarter plane