The number of rhyme schemes::Rhyme scheme


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The number of rhyme schemes

Tale of Genji chapter symbols, including diagrams of the first 52 set partitions

The number of different possible rhyme schemes for an n-line poem is given by the Bell numbers,<ref name="mg">{{#invoke:citation/CS1|citation |CitationClass=citation }}. Reprinted with an addendum as "The Tinkly Temple Bells", Chapter 2 of Fractal Music, Hypercards, and more ... Mathematical Recreations from Scientific American, W. H. Freeman, 1992, pp. 24–38.</ref> which for n = 1, 2, 3, ... are

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, … (sequence A000110 in OEIS).

For instance, there are five different rhyme schemes for a three-line poem: AAA, AAB, ABA, ABB, and ABC. Historically, the first exhaustive listing of rhyme schemes appears to be in the Tale of Genji, an 11th-century Japanese novel whose chapters are headed by diagrams representing the 52 rhyme schemes of a five-line poem.<ref name="mg"/> The number of rhyme schemes in which all lines rhyme with at least one other line is given by the numbers

0, 1, 1, 4, 11, 41, 162, 715, 3425, 17722, ... (sequence A000296 in OEIS).

For instance the four such rhyme schemes for a four-line poem are AABB, ABAB, ABBA, and AAAA. Both sequences of numbers may be found on either side of an augmented version of the Bell triangle.

Rhyme scheme sections
Intro   Function in writing   Example rhyme schemes  Rhyme schemes in hip-hop music  The number of rhyme schemes  References  External links  

The number of rhyme schemes
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