Guichard-Combinatorics-Graph-Theory · Problem 1.4.3
Fundamentals
Mathematics — Probability · bell-numbers-partitions
Problem
The rhyme scheme of a stanza of poetry indicates which lines rhyme. This is usually expressed in the form ABAB, meaning the first and third lines of a four line stanza rhyme, as do the second and fourth, or ABCB, meaning only lines two and four rhyme, and so on. A limerick is a five line poem with rhyming scheme AABBA. How many different rhyme schemes are possible for an n line stanza? To avoid duplicate patterns, we only allow a new letter into the pattern when all previous letters have been used to the left of the new one. For example, ACBA is not allowed, since when C is placed in position 2, B has not been used to the left. This is the same rhyme scheme as ABCA, which is allowed.