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 has genus one, and the step set is diagonally symmetric (i.e., with no steps in anti-diagonal directions). In that situation, after a transformation of the plane, we derive a quadrant-like functional equation. 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.

中文翻译：

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关于避开象限的四种对称行走模型的性质

我们研究了在四分之三平面上小步走的一些模型的生成序列的性质。更准确地说，我们将自己限制在群无穷大、核有属一、步集是对角对称的（即在对角线方向没有步长）的情况。在那种情况下，在平面变换之后，我们推导出一个象限式函数方程。在四种游走模型中，我们利用差分伽罗瓦理论得到其中三种具有微分超越生成级数，一种具有微分代数生成级数。