PlanetMath: part of a partition

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part of a partition

(Definition)

If $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_k)$ is an integer partition, then each $\lambda_j$ is a part of $\lambda$ . The length of $\lambda$ is defined as the number of its parts. If is the number of parts equal to , then the partition $\lambda$ is also written as $\lambda = (1^{m_1},2^{m_2},3^{m_3},\ldots)$ .

For example, if $\lambda=(5,4,4,4,3,3,3,3,3,1,1)$ then we also write $\lambda=(1^2,3^5,4^3,5^1)$ .

"part of a partition" is owned by drini. [ owner history (1) ]

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See Also: integer partition

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Cross-references: integer partition
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This is version 2 of part of a partition, born on 2005-02-10, modified 2005-02-12.
Object id is 6735, canonical name is Part.
Accessed 4655 times total.

Classification:

AMS MSC:	05A17 (Combinatorics :: Enumerative combinatorics :: Partitions of integers)
	11P99 (Number theory :: Additive number theory; partitions :: Miscellaneous)

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