Structure & Strangeness

 

: Distinct and Odd Partitions Puzzle : the set-up

: There is a direct mapping (bijection) of the set of Distinct Partitions of a
: number 'n' to the set of Odd Partitions of the same number. This process is
: also reversible (mathematically, the mapping is said to be one-to-one and
: onto). What is it?

: Definition: a 'Distinct Partition' of a number 'n' is a set of numbers whose
: sum is 'n' and whose elements are all distinct.

: Definition: an 'Odd Partition' of a number 'n' is a set of numbers whose sum
: is 'n' and whose elements are all odd (they may or may not be distinct).

: Example :

: The Distinct Partitions of 6:
: 6
: 5 1
: 4 2
: 3 2 1
: The Odd Partitions of 6:
: 5 1
: 3 3
: 3 1 1 1
: 1 1 1 1 1 1 1

: Good luck!

: To the answer

: [Credit: this puzzle was taken from the book "Generatingfunctionology"]

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© Aaron Clauset

updated 01.25.03