论文标题
高阶方程的轨道和方法
The Orbit-Sum Method for Higher Order Equations
论文作者
论文摘要
Orbit-sum方法是Bousquet-Mélou和Mishna引入的反射原理的代数版本，用于求解在刻板列出晶格步行中出现的功能方程，该步行的小步骤仅限于$ \ MATHBB {N}^2 $。 Bostan，Bousquet-Mélou和Melczer启动了它的大步走路。我们在此处继续它，利用原始元素定理，gröbner基碱和形状引理以及牛顿 - 普伊塞克斯算法。
The orbit-sum method is an algebraic version of the reflection-principle that was introduced by Bousquet-Mélou and Mishna to solve functional equations that arise in the enumeration of lattice walks with small steps restricted to $\mathbb{N}^2$. Its extension to walks with large steps was started by Bostan, Bousquet-Mélou and Melczer. We continue it here, making use of the primitive element theorem, Gröbner bases and the shape lemma, and the Newton-Puiseux algorithm.
