Partition

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

Table of contents

1 Mathematics
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 = x₀ < x₁ < ... < 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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