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arXiv:2110.01156math.CO

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

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

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Abstract

We examine and clarify in detail the contributions of Yoshisuke Matsunaga (1694?--1744) to the computation of Bell numbers in the eighteenth century (in the Edo period), providing modern perspectives to some unknown materials that are by far the earliest in the history of Bell numbers. Later clarification and developments by Yoriyuki Arima (1714--1783), and several new results such as the asymptotic distributions (notably the corresponding local limit theorems) of a few closely related sequences are also given.

arXiv comments
21 pages, 7 figures
Journal reference
DOI
Subjects
math.COCombinatorics math.HOHistory and Overview

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  1. The Art and Mathematics of Genji-Ko 1 comment

    • Obligatory entry in The On-Line Encyclopedia of Integer Sequences: https://oeis.org/A000110 which has 3 links mentioning Genji only one of which is not broken: Xiaoling Dou, Hsien-Kuei Hwang and Chong-Yi Li, Bell numbers in Matsunaga's and Arima's Genjiko combinatorics [1]…

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