Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

are * partition of a set or an

ordered partition In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a general ...

of a set, * partition of a graph, * partition of an integer, * partition of an interval, * partition of unity, * partition of a matrix; see

block matrix In mathematics, a block matrix or a partitioned matrix is a matrix that is '' interpreted'' as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original mat ...

, and *

partition of the sum of squares The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning of sums of squared deviations or errors. Mathematically, the sum of squared deviati ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

problems, especially in the

analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statisticia ...

, *

quotition and partition In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotition division one asks, "how many parts are there?"; While in partition division one asks, "what is the size of each part?". For example, the expressio ...

, two ways of viewing the operation of division of integers.

Integer partitions

Composition (number theory) In mathematics, a composition of an integer ''n'' is a way of writing ''n'' as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are ...

Ewens's sampling formula In population genetics, Ewens's sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample. Definition Ewens's sampling formula, introduced by Warren Ewens ...

* Ferrers graph *

Glaisher's theorem In number theory, Glaisher's theorem is an identity useful to the study of integer partitions. Proved in 1883 by James Whitbread Lee Glaisher, it states that the number of partitions of an integer n into parts not divisible by d is equal to the nu ...

Landau's function In mathematics, Landau's function ''g''(''n''), named after Edmund Landau, is defined for every natural number ''n'' to be the largest order of an element of the symmetric group ''S'n''. Equivalently, ''g''(''n'') is the largest least common mu ...

* Partition function (number theory) *

Pentagonal number theorem In mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function. It states that :\prod_^\left(1-x^\right)=\sum_^\left(-1\right)^x^=1+\sum_^\infty(-1)^k\left(x^+x^\right ...

Plane partition In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers \pi_ (with positive number, positive integer indices ''i'' and ''j'') that is nonincreasing in both indices. This means that : \pi ...

Quotition and partition In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotition division one asks, "how many parts are there?"; While in partition division one asks, "what is the size of each part?". For example, the expressio ...

* Rank of a partition ** Crank of a partition *

Solid partition In mathematics, solid partitions are natural generalizations of partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition of n is a three-dimensional array of non-negative integers n_ (with indices i, j, k\geq 1) su ...

* Young tableau * Young's lattice

Set partitions

{{main, Partition of a set * Bell number *

Bell polynomials In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in the Faà di Bruno's fo ...

** Dobinski's formula * Cumulant * Data clustering *

Equivalence relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. Each equivalence relation ...

Exact cover In the mathematical field of combinatorics, given a collection of subsets of a set , an exact cover is a subcollection of such that each element in is contained in ''exactly one'' subset in . In other words, is a partition of consisting of s ...

Knuth's Algorithm X Algorithm X is an algorithm for solving the exact cover problem. It is a straightforward recursive, nondeterministic, depth-first, backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the d ...

***

Dancing Links In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact ...

Exponential formula In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected str ...

* Faà di Bruno's formula *

Feshbach–Fano partitioning In quantum mechanics, and in particular in scattering theory, the Feshbach–Fano method, named after Herman Feshbach and Ugo Fano, separates (partitions) the resonant and the background components of the wave function and therefore of the associat ...

* Foliation *

Frequency partition In graph theory, a discipline within mathematics, the frequency partition of a graph ( simple graph) is a partition of its vertices grouped by their degree. For example, the degree sequence of the left-hand graph below is (3, 3, 3, 2, 2, 1) and it ...

* Graph partition *

Kernel of a function In set theory, the kernel of a function f (or equivalence kernel.) may be taken to be either * the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function f can tell",. or * the cor ...

Lamination (topology) In topology, a branch of mathematics, a lamination is a : * "topological space partitioned into subsets" * decoration (a structure or property at a point) of a manifold in which some subset of the manifold is partitioned into sheets of some low ...

Matroid partitioning Matroid partitioning is a problem arising in the mathematical study of matroids and in the design and analysis of algorithms. Its goal is to partition the elements of a matroid into as few independent sets as possible. An example is the problem of ...

* Multipartition *

Multiplicative partition In number theory, a multiplicative partition or unordered factorization of an integer ''n'' is a way of writing ''n'' as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. Th ...

* Noncrossing partition *

Ordered partition of a set In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a general ...

Partition calculus In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. Re ...

* Partition function (quantum field theory) *

Partition function (statistical mechanics) In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregat ...

Derivation of the partition function Derivation may refer to: Language * Morphological derivation, a word-formation process * Parse tree or concrete syntax tree, representing a string's syntax in formal grammars Law * Derivative work, in copyright law * Derivation proceeding, a proc ...

* Partition of an interval * Partition of a set **

Ordered partition In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a general ...

** Partition refinement ** Disjoint-set data structure *

Partition problem In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset ''S'' of positive integers can be partitioned into two subsets ''S''1 and ''S''2 such that the sum of the numbers ...

3-partition problem The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triplets that all have the same sum. More precisely: * The input to the problem ...

Partition topology In mathematics, the partition topology is a topology that can be induced on any set X by partitioning X into disjoint subsets P; these subsets form the basis for the topology. There are two important examples which have their own names: * The is ...

* Recursive partitioning *

Stirling number In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems. They are named after James Stirling, who introduced them in a purely algebraic setting in his book ''Methodus differentialis'' (1730). They were rediscov ...

Stirling transform In combinatorial mathematics, the Stirling transform of a sequence of numbers is the sequence given by :b_n=\sum_^n \left\ a_k, where \left\ is the Stirling number of the second kind, also denoted ''S''(''n'',''k'') (with a capital ''S''), which ...

* Stratification (mathematics) * Tverberg partition * Twelvefold way

In probability and stochastic processes

Chinese restaurant process In probability theory, the Chinese restaurant process is a discrete-time stochastic process, analogous to seating customers at tables in a restaurant. Imagine a restaurant with an infinite number of circular tables, each with infinite capacity. C ...

* Dobinski's formula *

Law of total cumulance In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. It has applications in the analysis of ti ...

Partition Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

Partition topics