# 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 |