Partition function (number theory): Difference between revisions

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=== Partition function in number theory ===

The '''partition [[function]]''' p(''n'') is a [[multiplicative function|non-multiplicative function]] and represents the [[number]] of possible [[integer partition|partitions]] of a [[natural number]] ''n'', which is to say the number of distinct (and order independent) ways of representing ''n'' as a [[sum]] of natural numbers. The partition function is easy to calculate. One way of doing so involves an intermediate function p(''k'',''n'') which represents the number of partitions of ''n'' using only natural numbers at least as large as ''k''. For any given value of ''k'', partitions counted by p(''k'',''n'') fit into exactly one of the following categories:

1. smallest [[addend]] is ''k''