Editing Bell number (section)

==History==
[[File:Genji chapter symbols groupings of 5 elements.svg|thumb|The traditional Japanese symbols for the 54 chapters of the ''Tale of Genji'' are based on the 52 ways of partitioning five elements (the two red symbols represent the same partition, and the green symbol is added for reaching 54).{{sfn|Knuth|2013}}]]
The Bell numbers are named after [[Eric Temple Bell]], who wrote about them in 1938, following up a 1934 paper in which he studied the [[Bell polynomials]].{{sfn|Bell|1934}}{{sfn|Bell|1938}} Bell did not claim to have discovered these numbers; in his 1938 paper, he wrote that the Bell numbers "have been frequently investigated" and "have been rediscovered many times". Bell cites several earlier publications on these numbers, beginning with {{harvnb|Dobiński|1877}} which gives [[Dobiński's formula]] for the Bell numbers. Bell called these numbers "exponential numbers"; the name "Bell numbers" and the notation ''B<sub>n</sub>'' for these numbers was given to them by {{harvnb|Becker|Riordan|1948}}.<ref>{{harvnb|Rota|1964}}. However, Rota gives an incorrect date, 1934, for {{harvnb|Becker|Riordan|1948}}.</ref>

The first exhaustive enumeration of set partitions appears to have occurred in medieval Japan, where (inspired by the popularity of the book ''[[The Tale of Genji]]'') a parlor game called ''[[Kōdō#Monkō|genjikō]]'' sprang up, in which guests were given five packets of incense to smell and were asked to guess which ones were the same as each other and which were different. The 52 possible solutions, counted by the Bell number ''B''<sub>5</sub>, were recorded by 52 different diagrams, which were printed above the chapter headings in some editions of ''The Tale of Genji.''{{sfn|Knuth|2013}}<ref>{{harvnb|Gardner|1978}} and {{harvnb|Berndt|2011}} also mention the connection between Bell numbers and ''The Tale of Genji,'' in less detail.</ref>

In [[Srinivasa Ramanujan]]'s second notebook, he investigated both Bell polynomials and Bell numbers.{{sfn|Berndt|2011}}
Early references for the [[Bell triangle]], which has the Bell numbers on both of its sides, include {{harvnb|Peirce|1880}} and {{harvnb|Aitken|1933}}.