Of Thee I Sing
A set of four elements can be partitioned in exactly 15 ways. Pleasingly, that's also the number of rhyme schemes a 4-line poem can take — one partition per scheme, since a scheme is really just a way of grouping four lines into rhyming sets:
- AAAA
- AAAB
- AABA
- AABB
- AABC
- ABAA
- ABAB
- ABAC
- ABBA
- ABBB
- ABBC
- ABCA
- ABCB
- ABCC
- ABCD
A 5-line poem has 52 possible schemes, matching the partitions of a 5-element set, and so on upward. These counts are called Bell numbers.
Based on a post on Futility Closet.