The Fractal Nature of Partitions

Rewrite the following partition of 21 as a dot product of frequencies and parts: . The sum of the frequencies is 7.

Partitions are listed in reverse lexicographic order. For example, the five partitions of 4 are listed as .

For each , this Demonstration plots (from the bottom to the top) the means, medians, and sums of the nonzero frequencies of the parts of the partitions of .