Partition

In general, a partition is a splitting into parts. The word partition has technical meanings in mathematics, computer science, politics, and 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 set of functions 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

• Partition (computing), the dividing of a hard disk's 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) use 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.