2019/11/15 by Hsien‐Kuei Hwang, Hsien-Kuei Hwang, Hwang, Hsien-Kuei +2
Mathematics · #05A05 #05A15 #05A16 #11M50 #11P82 #60C05 #60F05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Applied mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limit (mathematics) #Mathematical analysis #Mathematical optimization #Mathematics #Modular form #Number Theory (math.NT) #Point (geometry) #Probability (math.PR) #Pure mathematics #Random Matrices and Applications #Saddle #Saddle point #math.CO #math.NT #math.PR #msc:05A05 #msc:05A15 #msc:05A16 #msc:11M50 #msc:11P82 #msc:60C05 #msc:60F05
paper · pdf · doi:10.48550/arxiv.1911.06690
44 pages, 20 figures
openalex publication_date 2019/11/15 · openalex created_date 2019/11/22 · arxiv created 2020/10/13 · arxiv updated 2020/10/14 · openalex updated_date 2026/08/06
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.