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: 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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