info prev up next book cdrom email home

Elder's Theorem

A generalization of Stanley's Theorem. It states that the total number of occurrences of an Integer $k$ among all unordered Partitions of $n$ is equal to the number of occasions that a part occurs $k$ or more times in a Partition, where a Partition which contains $r$ parts that each occur $k$ or more times contributes $r$ to the sum in question.

See also Stanley's Theorem


Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer, pp. 8-9, 1985.

© 1996-9 Eric W. Weisstein