Partition function (number theory): Difference between revisions

Revision as of 00:17, 3 August 2023

Revision as of 08:57, 3 September 2023

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As base cases, <math>p(0)</math> is taken to equal <math>1</math>, and <math>p(k)</math> is taken to be zero for negative&nbsp;<math>k</math>. Although the sum on the right side appears infinite, it has only finitely many nonzero terms,

coming from the nonzero values of <math>k</math> in the range

<math display="block"> - \frac{\sqrt{24n+1}-+1}{6} \leq k \leq \frac{\sqrt{24n+1}+1}{6}.</math>

Another recurrence relation for <math>p(n)</math> can be given in terms of the [[divisor function|sum of divisors function]] {{math|''σ''}}:{{r|wilf}}