WOLFRAM|DEMONSTRATIONS PROJECT

The Fractal Nature of Partitions

​
n
10
Rewrite the following partition of 21 as a dot product of frequencies and parts:
1+1+1+2+4+4+8=3×1+1×2+2×4+1×8=(3,1,0,2,0,0,0,1,0,0,0,…,0)·(1,2,3,4,…,21)
. The sum of the frequencies is 7.
Partitions are listed in reverse lexicographic order. For example, the five partitions of 4 are listed as
4,3+1,2+2,2+1+1,1+1+1+1
.
For each
n
, 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
n
.