Asymptotics and statistics on Fishburn matrices and their generalizations
Combinatorics
2020-10-14 v2 Number Theory
Probability
Abstract
A direct saddle-point analysis (without relying on any modular forms, identities or functional equations) is developed to establish the asymptotics of Fishburn matrices and a large number of other variants with a similar sum of-finite-product form for their (formal) general functions. In addition to solving some conjectures, the application of our saddle-point approach to the distributional aspects of statistics on Fishburn matrices is also examined with many new limit theorems characterized, representing the first of their kind for such structures.
Cite
@article{arxiv.1911.06690,
title = {Asymptotics and statistics on Fishburn matrices and their generalizations},
author = {Hsien-Kuei Hwang and Emma Yu Jin},
journal= {arXiv preprint arXiv:1911.06690},
year = {2020}
}
Comments
44 pages, 20 figures