标题： 连通性的渐近概率 显示英文标题

标题： Asymptotic probability for connectedness

摘要： 我们研究组合对象连通概率渐近展开的结构。 我们证明这些渐近中出现的系数是整数，并且可以解释为其他导出组合类的计数序列。 一般性结果适用于快速增长的组合结构，我们称之为巨大型结构，它们也允许序列分解。 该结果随后被应用于几种图模型、曲面模型（正方形镶嵌曲面、组合地图）以及高维几何模型（星形图、图编码流形）。 相应的导出组合类是不可约的（多）竞赛图、不可分解的（多）排列和不可分解的完美（多）匹配。 显示英文摘要

摘要： We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of other derivative combinatorial classes. The general result applies to rapidly growing combinatorial structures, which we call gargantuan, that also admit a sequence decomposition. The result is then applied to several models of graphs, of surfaces (square-tiled surfaces, combinatorial maps), and to geometric models of higher dimension (constellations, graph encoded manifolds). The corresponding derivative combinatorial classes are irreducible (multi)tournaments, indecomposable (multi)permutations and indecomposable perfect (multi)matchings.