论文标题
关于鱼潮矩阵的渐近学和统计数据：尺寸分布和stoimenow的猜想
Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow
论文作者
论文摘要
我们通过复杂的分析方法建立了大尺寸随机鱼卷矩阵的渐近正态性。还解决了大小下大小分布的相应双重问题，并遵循二次类型的正常极限定律。这些结果代表了同类产品中的第一个，并解决了组合文献中提出的两个开放问题。它们是在一个通用框架中呈现的，该框架不限于二元或非负整数。我们采用的分析性鞍点方法是基于由于安德鲁斯和耶利尼克引起的$ q $ series的强大转换，也可用于求解Vassiliev不变性的Stoimenow的猜想。
We establish the asymptotic normality of the dimension of large-size random Fishburn matrices by a complex-analytic approach. The corresponding dual problem of size distribution under large dimension is also addressed and follows a quadratic type normal limit law. These results represent the first of their kind and solve two open questions raised in the combinatorial literature. They are presented in a general framework where the entries of the Fishburn matrices are not limited to binary or nonnegative integers. The analytic saddle-point approach we apply, based on a powerful transformation for $q$-series due to Andrews and Jelínek, is also useful in solving a conjecture of Stoimenow in Vassiliev invariants.
