Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in
mathematics are
*
partition of a set or an
ordered partition of a set,
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partition of a graph,
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partition of an integer,
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partition of an interval,
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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 ma ...
, and
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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 ...
in
statistics 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 statistician ...
,
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quotition and partition, two ways of viewing the operation of division of integers.
Integer partitions
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Composition (number theory)
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Ewens's sampling formula
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Ferrers graph
In number theory and combinatorics, a partition of a positive integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same parti ...
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Glaisher's theorem
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Landau's function
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Partition function (number theory)
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Pentagonal number theorem
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Plane partition
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Quotition and partition
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Rank of a partition
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Crank of a partition
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Solid partition
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Young tableau
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Young's lattice
Set partitions
{{main, Partition of a set
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Bell number
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Bell polynomials
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Dobinski's formula
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Cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the '' moments'' of the distribution. Any two probability distributions whose moments are identical will hav ...
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Data clustering
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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 relatio ...
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Exact cover
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Knuth's Algorithm X
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Dancing Links
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Exponential formula
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Faà di Bruno's formula
Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives. It is named after , although he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French ...
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Feshbach–Fano partitioning
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Foliation
In mathematics ( differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition ...
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Frequency partition
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Graph partition
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Kernel of a function
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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 lo ...
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Matroid partitioning
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Multipartition In number theory and combinatorics, a multipartition of a positive integer ''n'' is a way of writing ''n'' as a sum, each element of which is in turn a partition. The concept is also found in the theory of Lie algebras.
r-component multipartition ...
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Multiplicative partition
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Noncrossing partition
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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 ...
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Partition calculus
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Partition function (quantum field theory)
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Partition function (statistical mechanics)
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Derivation of the partition function
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Partition of an interval
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Partition of a set
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Ordered partition
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Partition refinement
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Disjoint-set data structure
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Partition problem
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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 ...
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Partition topology
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Quotition and partition
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Recursive partitioning
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Stirling number
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Stirling transform
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Stratification (mathematics)
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Tverberg partition
In discrete geometry, Tverberg's theorem, first stated by , is the result that sufficiently many points in ''d''-dimensional Euclidean space can be partitioned into subsets with intersecting convex hulls. Specifically, for any set of
:(d + 1)(r ...
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Twelvefold way
In probability and stochastic processes
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Chinese restaurant process
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Dobinski's formula
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Ewens's sampling formula
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Law of total cumulance
Partition
Partition topics