Margaret Kepner

In addition to other properties, the fifth Bell Number counts the ways in which the last word of a five-line poem can rhyme. A poem with no rhyming lines can be represented by abcde, while a limerick would read aabba. In this piece, each of the 52 possible five-line rhyme schemes is depicted by a color-coded square of rectangles. Black vertical bars (B) indicate the positions of the first rhyme sound, while the white bars (W) show the second rhyme sound, if needed. Thus, the limerick (row 6, column 4) appears as BBWWB. The horizontal bars show the line-count and span of each rhyming sound. In this example, the upper yellow bar denotes a rhyme with 3 lines and a span of 5; the lower red bar corresponds to a 2-line rhyme with a span of 2.

The Bell Numbers can be visualized in a lattice format, with nodes and lines. In this piece, 52 nodes are shown, each representing a partition of 5 elements into subsets. They are positioned as they would be in a lattice diagram, but with the lines omitted. Each node/circle depicts a rhyme scheme for a 5-line poem. Concentric rings are colored to indicate similar rhyme sounds in the poem. The limerick pattern appears in the 2nd element of row 4. Moving inward, the concentric rings are colored RRGGR. They are partially transparent to allow visual color mixing. Starting with the all-gray circle at the top (no rhymes), each successive row includes more rhyming lines (and thus colors). For the bottom element, colored RRRRR, all lines rhyme.