Bell numbers in Matsunaga's and Arima's Genjikō combinatorics: modern perspectives and local limit theorems

DOI10.37236/10762OpenAlexW3202786568WikidataQ113693645 ScholiaQ113693645MaRDI QIDQ2138555

Hsien-Kuei Hwang, Chong-Yi Li, Xiaoling Dou

Publication date: 12 May 2022

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.01156

Mathematics Subject Classification ID

Strong limit theorems (60F15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Combinatorial probability (60C05) Asymptotic enumeration (05A16) History of combinatorics (05-03) History of Japanese mathematics (01A27)

Uses Software

• OEIS

Cites Work

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• The \(r\)-Stirling numbers
• On convergence rates in the central limit theorems for combinatorial structures
• On the Lambert \(w\) function
• Asymptotic expansions for the Stirling numbers of the first kind
• An asymptotic distribution theory for Eulerian recurrences with applications
• Central and local limit theorems applied to asymptotic enumeration
• The iterated exponential integers
• Commutation Relations, Normal Ordering, and Stirling Numbers
• The $r$-Bell numbers
• Asymptotic Estimates of Stirling Numbers
• Two Notes on Notation
• Asymptotic Development of the Stirling Numbers of the First Kind
• Local Limit Theorems for the Number of Components of Random Permutations and Mappings
• Combinatorics of Set Partitions
• The Number of Partitions of a Set
• The Arithmetic of Bell and Stirling Numbers

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