Partition function (number theory): Difference between revisions

Revision as of 15:42, 23 December 2003

Revision as of 15:43, 23 December 2003

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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. By convention p(0) = 1, p(<i>''n</i>'') = 0 for <i>''n</i>'' negative.

One way of getting a handle on the partition function 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: