Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
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Euler’s Partition Theorem:<br />
The number <strong>of</strong> <strong>partition</strong>s <strong>of</strong> an integer N into odd parts is equal<br />
to <strong>the</strong> number <strong>of</strong> <strong>partition</strong>s <strong>of</strong> N into distinct parts.<br />
Example: N = 8<br />
Odd parts:<br />
(7,1) (5,3) (5,1,1,1) (3,3,1,1) (3,1,1,1,1,1) (1,1,1,1,1,1,1,1)<br />
Distinct Parts:<br />
(8) (7,1) (6,2) (5,3) (5,2,1) (4,3,1)