# part of a partition

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 $m_{j}$ is the number of parts equal to $j$, then the partition $\lambda$ is also written as $\lambda=(1^{m_{1}},2^{m_{2}},3^{m_{3}},\ldots)$.

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

Title part of a partition PartOfAPartition 2013-03-22 15:01:34 2013-03-22 15:01:34 drini (3) drini (3) 5 drini (3) Definition msc 11P99 msc 05A17 IntegerPartition length