论文标题
象限步行从象限外面开始
Quadrant Walks Starting Outside the Quadrant
论文作者
论文摘要
我们研究了一个功能方程，该方程类似于四分之一平面的晶格步行模型的生成函数的功能方程。该方程的有趣特征是其轨道总和为零，而其解决方案不是代数。该解决方案可以解释为$ \ mathbb {z}^2 $以$（ - 1，-1）$的生成函数，并受到只能在一个方向上越过坐标轴的限制。我们还考虑了方程式的某些变体，所有方程似乎都具有先验解决方案。在一种情况下，解决方案也许甚至不是d-finite。
We investigate a functional equation which resembles the functional equation for the generating function of a lattice walk model for the quarter plane. The interesting feature of this equation is that its orbit sum is zero while its solution is not algebraic. The solution can be interpreted as the generating function of lattice walks in $\mathbb{Z}^2$ starting at $(-1,-1)$ and subject to the restriction that the coordinate axes can be crossed only in one direction. We also consider certain variants of the equation, all of which seem to have transcendental solutions. In one case, the solution is perhaps not even D-finite.
