论文标题
Kreweras步行与相互作用边界的生成功能不是代数
The generating function of Kreweras walks with interacting boundaries is not algebraic
论文作者
论文摘要
Beaton，Owczarek和Xu（2019）研究了Kreweras Walks的生成功能，并在四分之一飞机上进行了反向Kreweras Walks的互动界限。他们证明，对于反向Kreweras步骤集，生成函数始终为代数，对于Kreweras步骤集，生成函数始终为d-Finite。但是，除了在$ x $和〜$ y $中对称的特定情况外，他们留下了一个问题，即后者是否是代数。使用计算机代数工具，我们确认他们的直觉是，除了已经确定的特定情况外，Kreweras Walks的生成功能不是代数。
Beaton, Owczarek and Xu (2019) studied generating functions of Kreweras walks and of reverse Kreweras walks in the quarter plane, with interacting boundaries. They proved that for the reverse Kreweras step set, the generating function is always algebraic, and for the Kreweras step set, the generating function is always D-finite. However, apart from the particular case where the interactions are symmetric in $x$ and~$y$, they left open the question of whether the latter one is algebraic. Using computer algebra tools, we confirm their intuition that the generating function of Kreweras walks is not algebraic, apart from the particular case already identified.
