# Partition

**has technical meanings in mathematics, computer science, and politics.**

*Partition*

Table of contents |

2 Computer science 3 Politics 4 Music |

## Mathematics

*See also*

*list of partition topics*

- A partition of a set
*X*is a collection of non-empty subsets of*X*such that every element of*X*belongs to one and only one of the subsets. - A partition of a number is a way to write a positive integer as a sum of other positive integers.
- The partition function in number theory is the function which for every positive integer gives the number of different ways to partition that number (in the sense above).
- A partition of unity is a any set of functionss whose sum is the constant function 1. The functions may be required to have additional properties such as continuity, smoothness, or non-negativity.
- The
**PARTITION**problem is to divide a list of positive integers into two parts so that the sums of the numbers in the two parts are equal. It is a common example of an NP-complete problem, often useful in proving that other problems are NP-complete. - A partition of an interval [
*a*,*b*] on the real line is a finite increasing sequence of numbers*a*=*x*_{0}<*x*_{1}< ... <*x*_{n−1}<*x*_{n}=*b*. Such partitions are used in the theory of the Riemann integral and the Riemann-Stieltjes integral, and in numerical computations with such integrals.

## Computer science

- Hard disk drive partitioning, dividing a hard disk storage space into independent parts called "partitions".
- Partition (IBM PC), one of those storage space parts.
- for dividing a big computer (e.g. a mainframe) into several independent virtual computers, see also LPAR, IBM mainframe, Sun E10.000, HP-UX. Some vendors (e.g. Sun) uses the term
**domain**instead of partition.

## Politics

- The Partitions of Poland
- The 1947 UN Partition Plan for Palestine
- The 1947 Partition of India and Pakistan
- The Partition of Ireland into the 26 counties of the Irish Free State and the 6 counties of Northern Ireland

## Music

- In music using the twelve tone technique the use of methods to create segments from sets, most often through registral difference. The opposite of derivation used in derived rows.
- More generally, in musical set theory partitioning is the division of the domain of pitch class sets into types, such as transpositional type, see equivalence class and cardinality.

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