论文标题
带有一个催化变量的阳性功能方程的通用渐近特性
Universal asymptotic properties of positive functional equations with one catalytic variable
论文作者
论文摘要
具有一种催化的功能方程出现在几种组合应用中，最著名的是在晶格路径的枚举和平面图的枚举中。本文的主要目的是表明，在某些阳性假设下，解决方案的主要奇异性具有普遍的行为。我们必须区分出现主导平方根奇异性的线性催化方程，而非线性催化方程，我们通常（通常）具有3/2型的奇异性。
Functional equations with one catalytic appear in several combinatorial applications, most notably in the enumeration of lattice paths and in the enumeration of planar maps. The main purpose of this paper is to show that under certain positivity assumptions the dominant singularity of the solutions have a universal behavior. We have to distinguish between linear catalytic equations, where a dominating square root singularity appears, and non-linear catalytic equations, where we - usually - have a singularity of type 3/2.
