Partition function: Difference between revisions

Revision as of 20:38, 18 September 2002

Revision as of 02:38, 15 October 2002

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''The partition function described here is part of [[number theory]]. The present author has absolutely no idea whether this is the same function referred to as a partition function in [[derivation of the partition function|statistical mechanics]] or [[partition function game|game theory]].''

The partition [[function]] p(''n'') is a [[multiplicative function|non-multiplicative function]] and represents the [[number]] of possible [[integer partition|partitions]]s 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''