Of Thee I Sing

A set of 4 elements can be partitioned in 15 ways. Pleasingly, this is also the number of rhyme schemes that a 4-line poem can take: AAAA, AAAB, AABA, AABB, AABC, ABAA, ABAB, ABAC, ABBA, ABBB, ABBC, ABCA, ABCB, ABCC, ABCD. A poem with 5 lines has 52 possible schemes, corresponding to the partitions …

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