User Contributed Dictionary

English

partitions

partitions

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

Partition (law), to divide up a piece of land into separate portions representing the proportionate interests of the tenants. It may also consist of dividing a property with common ownership into identifiable individual ownership

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
Multiplicative partition, a way to write an integer greater than 1 as a product of other integers that are also greater than 1.
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 (music) — a method of creating segments from sets when the twelve-tone technique is used

Notable examples are:

Partitions of Poland and Poland-Lithuania in the 18th, 19th and 20th centuries
1905 Partition of Bengal and 1947 Partition of Bengal
Partition of India (colonial British India) in 1947 into the independent dominions (later republics) of India and Pakistan (which included modern day Bangladesh)
Partition of Punjab in 1966 into the states of Punjab, Haryana and Himachal Pradesh
Partition of Pakistan in 1971, when East Pakistan became the independent nation of Bangladesh after the Bangladesh Liberation War
1947 UN Partition Plan for Palestine (region)
Partition of Ireland in 1920 into the independent Irish Free State and (British) Northern Ireland
Treaty of Kars of 1921, which partitioned Ottoman Armenia between the republic of Turkey and the then Soviet Union (Western and Eastern Armenia)
Partition of Vietnam in 1954
Partitions of Luxembourg, last in 1838 into Duchy of Luxembourg and Belgian province
The hypothetical partition of the Canadian province of Quebec