Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow

Autor:	Hwang, Hsien-Kuei, Jin, Emma Yu, Schlosser, Michael J.
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics 05A16 05A15 60C05 60F05
Druh dokumentu:	Working Paper
Popis:	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 Jel\'inek, is also useful in solving a conjecture of Stoimenow in Vassiliev invariants. Comment: 35 pages, comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.13570 Zobrazit plný text záznamu View this record from Arxiv