partició

Partició is a concept used in mathematics and related fields to describe a way of dividing a set into smaller, nonempty pieces that do not overlap and together cover the entire original set. Each resulting piece is called a block or part of the partition. The arrangement is not about the order of the blocks, only about which elements belong together.

In set theory and combinatorics, a partition of a set S is a collection of nonempty, pairwise disjoint subsets whose union is S. A fundamental fact is the correspondence between partitions and equivalence relations: every partition induces an equivalence relation where elements are related if they lie in the same block, and conversely each equivalence relation partitions the set into equivalence classes. The number of partitions of a set with n elements is the Bell number B_n. The number of partitions of an n-element set into k blocks is given by the Stirling number of the second kind S(n,k).

A related but distinct notion is the integer partition. A partition of a positive integer n expresses n as a sum of positive integers in which order does not matter (for example, 4 = 4, 3+1, 2+2, 2+1+1, 1+1+1+1). The function p(n) counts such partitions, with various generating functions and combinatorial interpretations. Partitions are used in number theory, combinatorics, probability, and data analysis, often serving as a way to organize elements into meaningful groups.

In computing, partitioning also refers to dividing a storage medium into separate regions or partitions, enabling independent file systems, permissions, or boot configurations. The specifics depend on the system, such as MBR or GPT partitioning schemes.