加权象限游走的枚举：代数性与D-有限性的判据
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
更新
AI总结：
本文提出基于椭圆函数理论的统一方法，为象限内加权游走生成函数的代数性与D-有限性判定提供统一证明。
AI中文摘要：
在限制于象限平面内的加权游走枚举领域，已知生成函数的行为因所选步集的不同而差异显著；实践中，文献中使用的技术取决于计数级数的复杂度。本文引入一种基于椭圆函数理论的统一方法，使我们能够对生成函数的代数性与D-有限性的刻画给出统一的证明。
英文摘要：
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on the complexity of the counting series. In this paper we introduce a unified approach based on the theory of elliptic functions, which allows us to have a common proof of the characterisation of the algebraicity and D-finiteness of the generating functions.
