partition

Partition is a term with multiple meanings, generally referring to the act of dividing a whole into parts, or the resulting parts. It can denote a division process in everyday language as well as formal concepts in various disciplines.

In mathematics, a partition of a set is a collection of nonempty disjoint subsets whose union is the entire set. Partitions correspond to equivalence relations, with each block representing an equivalence class; the number of partitions of a finite set with n elements is given by the Bell numbers. A partition of a positive integer expresses it as a sum of positive integers where order does not matter; for example, 4 can be partitioned as 3+1, 2+2, 2+1+1, or 1+1+1+1. The partition function p(n) counts such decompositions, and generating functions are used to study their properties. In topology and geometry, a partition of a space is a division into disjoint nonempty subsets whose union is the whole space.

In computer science and information technology, a disk partition divides a storage device into independent sections, which may be designated as primary, extended, or logical, depending on the partitioning scheme (MBR or GPT). Partitions allow separate operating systems, file systems, or data to be managed independently. In databases, partitioning (or sharding) distributes data across multiple storage units to improve performance and scalability.

Geopolitically, partition refers to the division of a polity into separate political entities, often along borders, such as the Partition of India in 1947. In music, a partition can denote a written score or sheet music that delineates parts for performers.