Partition

Related Topics:
Partition :: Partitions

Generally, a partition is a splitting of something into parts. The term is used in a variety of senses:

List of partition topics
Partition of a set, a collection of non-empty subsets such that every element belongs to one and only one of the subsets
Partition (number theory), a way to write a positive integer as a sum of other positive integers; the partition function gives the number of different ways to partition a number
Partition problem, an NP-complete problem: given a set of integers, can the set be partitioned into two subsets with equal sums?
A partition of unity is a set of functions whose sum is the constant function
Partition of an interval, used in the theory of the Riemann integral and the Riemann-Stieltjes integral

Partition (computing), the dividing of a hard disk's storage space into independent parts
Partition (mainframe), for dividing a computer into several independent virtual computers
Partition also refers to an algorithm used in quicksort which separates a list into two sublists, those elements less than or equal to a value and those greater than it. It is also used in selection algorithms.
Partition (database) for splitting a database.
Partition problem, an NP-complete problem: given a set of integers, can the set be partitioned into two subsets with equal sums?

Notable examples are:

Partitions of Poland and Poland-Lithuania in the 18th, 19th and 20th centuries
1947 UN Partition Plan for Palestine (region)
Partition of India (colonial British India) in 1947 into the independent dominions (later republics) of India and Pakistan (then still including East Pakistan, the present Bangladesh)
Partition of Ireland in 1920 into the independent Irish Free State and Northern Ireland which remains part of the U.K.
Treaty of Kars of 1921, which partioned Ottoman Armenia between the republic of Turkey and the then Soviet Union (Western Armenia|Western and Eastern Armenia)

Partition (law), to divide up a piece of land into separate portions representing the proportionate interests of the tenants

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.
an old name for types of compositions in several parts; there is no fixed meaning, and in several cases the term was reportedly interchanged with various other terms

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