part of a partitionPart2005-02-10 12:28:092005-02-12 20:28:18Definitioninteger partitionlength\usepackage{graphicx}
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\newtheorem{dfn}{Definition}If $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_k)$ is an integer partition, then each $\lambda_j$ is a \emph{part} of $\lambda$. The \emph{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 $\lambda=(1^2,3^5,4^3,5^1)$.