论文标题
关于四个型号的对称步行的性质，避免了象限
On the nature of four models of symmetric walks avoiding a quadrant
论文作者
论文摘要
我们研究了在三分之一平面中具有小步骤的某些型号的生成系列的性质。更确切地说，我们将自己限制在群体是无限的情况下，内核具有属，并且步骤集是对角线对称的（即，在反迪亚角方向上没有步骤）。在这种情况下，在平面转换之后，我们得出了一个象限的功能方程。在四种散步模型中，我们使用差异理论获得，其中三个具有差异性先验生成系列，一个具有差异化代数生成系列。
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.
