A couple years ago I made a codepen to generate arbitrarily long Genji-mon from a ruleset, and managed to write a rule that reduces the number of required special cases to one. However, these rules are very fragile, and "break" with lengths > 5 (edit: or maybe they don't! this deserves further exploration). Glad to see someone else discovering the structure behind this interesting system!
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]: Modern perspectives and local limit theorems, arXiv:2110.01156 [math.CO], 2021.
A couple years ago I made a codepen to generate arbitrarily long Genji-mon from a ruleset, and managed to write a rule that reduces the number of required special cases to one. However, these rules are very fragile, and "break" with lengths > 5 (edit: or maybe they don't! this deserves further exploration). Glad to see someone else discovering the structure behind this interesting system!
https://codepen.io/rezmason/pen/ejWogV
Loved this. Great writing and a bit of cultural arcana I knew nothing about but which resonates into the present day.
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]: Modern perspectives and local limit theorems, arXiv:2110.01156 [math.CO], 2021.
[1] https://arxiv.org/abs/2110.01156