## § Odd partitions, unique partitions

A well known identity in combinatorics is that the partitions n = l1 + l2 + ... + ln where each li is odd is in bijectiion with a partition where each li is unique. I really liked this bijection.
(15, 9, 9, 5, 5, 5, 3, 3, 3, 1, 1, 1, 1) [all odd]
=
(15, 9x2, 5x3, 3x3, 1x4) [group]
=
(15x1, 9x2, 5x(2+1), 3x(2+1), 1x4) [expand base-2]
=
(15, 18, [10, 5], [6, 3], 4) [all unique]