part of a partition

If $\lambda =({\lambda }_1,{\lambda }_2,\mathrm{\dots },{\lambda }_k)$ 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 $m_j$ is the number of parts equal to $j$, then the partition $\lambda$ is also written as $\lambda =(1^{m_1},2^{m_2},3^{m_3},\mathrm{\dots })$.

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

Title	part of a partition
Canonical name	PartOfAPartition
Date of creation	2013-03-22 15:01:34
Last modified on	2013-03-22 15:01:34
Owner	drini (3)
Last modified by	drini (3)
Numerical id	5
Author	drini (3)
Entry type	Definition
Classification	msc 11P99
Classification	msc 05A17
Related topic	IntegerPartition
Defines	length