Asymptotics and statistics on Fishburn matrices and their generalizations
| Autor: | Hsien-Kuei Hwang, Emma Yu Jin |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
05A16
11P82 05A05 05A15 11M50 60C05 60F05 Modular form 0102 computer and information sciences q-series 01 natural sciences Theoretical Computer Science Statistics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Number Theory (math.NT) Limit (mathematics) 0101 mathematics Fishburn matrices Saddle Mathematics Stirling statistics Mathematics - Number Theory Fishburn numbers Probability (math.PR) 010102 general mathematics Generating functions Computational Theory and Mathematics 010201 computation theory & mathematics Combinatorics (math.CO) Mathematics - Probability Saddle-point method |
| Zdroj: | Journal of Combinatorial Theory, Series A. 180:105413 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2021.105413 |
| Popis: | 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. Comment: 44 pages, 20 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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