Geodesic
Bell numbers in Matsunaga's and Arima's Genjikō combinatorics: modern perspectives and local limit theorems
Xiaoling Dou1 ; Hsien-Kuei Hwang2 ; Chong-Yi Li3
1Center for Data Science, Waseda University
2Academia Sinica
3Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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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.
DOI : 10.37236/10762
Classification : 05-03, 01A27, 05A16, 41A60, 60C05, 60F15

Xiaoling Dou  1   ; Hsien-Kuei Hwang  2   ; Chong-Yi Li  3

1 Center for Data Science, Waseda University
2 Academia Sinica
3 Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan 
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     author = {Xiaoling Dou and Hsien-Kuei Hwang and Chong-Yi Li},
     title = {Bell numbers in {Matsunaga's} and {Arima's} {Genjik\={o}} combinatorics: modern perspectives and local limit theorems},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/10762},
     zbl = {1531.05002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10762/}
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Xiaoling Dou; Hsien-Kuei Hwang; Chong-Yi Li. Bell numbers in Matsunaga's and Arima's Genjikō combinatorics: modern perspectives and local limit theorems. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10762

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