On the nature of four models of symmetric walks avoiding a quadrant
Sprache des Titels:
We study the nature of the generating series of some models of walks with small steps in the three quarter plane. More precisely, we restrict ourselves to the situation where the group is infinite, the kernel have genus one, and the step set is symmetric, with no anti-diagonal directions. In that situation, a functional equation can be solved. Among the four models of walks, we obtain, using difference Galois theory, that three of them have a differentially transcendental generating series, and one has a differentially algebraic generating series.