• a partition of a set
  Partition of a set
  In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...
  
   or an ordered partition of a set, or
• a partition of a graph
  Graph partition
  In mathematics, the graph partition problem is defined on data represented in the form of a graph G= , with V vertices and E edges, such that it is possible to partition G into smaller components with specific properties. For instance, a k-way partition divides the vertex set into k smaller...
  
  , or
• a partition of an integer
  Partition (number theory)
  In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered to be the same partition; if order matters then the sum becomes a...
  
  , or
• a partition of an interval
  Partition of an interval
  In mathematics, a partition, P of an interval [a, b] on the real line is a finite sequence of the formIn mathematics, a partition, P of an interval [a, b] on the real line is a finite sequence of the form...
  
  , or
• a partition of unity, or
• a partition of a matrix; see block matrix
  Block matrix
  In the mathematical discipline of matrix theory, a block matrix or a partitioned matrix is a matrix broken into sections called blocks. Looking at it another way, the matrix is written in terms of smaller matrices. We group the rows and columns into adjacent 'bunches'. A partition is the rectangle...
  
  , or
• a partition of the sum of squares in statistics
  Statistics
  Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
  
   problems, especially in the analysis of variance
  Analysis of variance
  In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
  
  .

List of topics

• Bell number
  Bell number
  In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it...
  
   
  • Dobinski's formula 
• Chinese restaurant process 
• Cumulant
  Cumulant
  In probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. The moments determine the cumulants in the sense that any two probability distributions whose moments are identical will have...
  
   
• Data clustering
  Data clustering
  Cluster analysis or clustering is the task of assigning a set of objects into groups so that the objects in the same cluster are more similar to each other than to those in other clusters....
  
  
• Equivalence relation
  Equivalence relation
  In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell...
  
   
• Ewens's sampling formula
  Ewens's sampling formula
  In population genetics, Ewens' sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.-Definition:...
  
   
• Exact cover 
  • Knuth's Algorithm X
    Knuth's Algorithm X
    Donald Knuth's Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem represented by a matrix A consisting of 0s and 1s...
    
     
    • Dancing Links
      Dancing Links
      In computer science, Dancing Links, also known as DLX, is the technique suggested by Donald Knuth to efficiently implement his Algorithm X. Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem...
      
       
• Exponential formula
  Exponential formula
  In combinatorial mathematics, the exponential formula states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.The exponential formula is a power-series version of a special case of Faà di...
  
   
• Faà di Bruno's formula
  Faà di Bruno's formula
  Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after , though he was not the first to state or prove the formula...
  
   
• Ferrers graph 
• Frequency partition
  Frequency partition
  In graph theory, a discipline within mathematics, the frequency partition of a graph is a partition of its vertices grouped by their degree.For example, the degree sequence of the left-hand graph below is and its frequency partition is 6 = 3 + 2 + 1...
  
   
• Glaisher's theorem 
• Graph partition
  Graph partition
  In mathematics, the graph partition problem is defined on data represented in the form of a graph G= , with V vertices and E edges, such that it is possible to partition G into smaller components with specific properties. For instance, a k-way partition divides the vertex set into k smaller...
  
   
• Integer partition 
• Kernel of a function
  Kernel of a function
  In set theory, the kernel of a function f 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 corresponding partition of the domain....
  
   
• Landau's function
  Landau's function
  In mathematics, Landau's function g, named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn...
  
   
• Law of total cumulance
  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 time series...
  
   
• Multiplicative partition
  Multiplicative partition
  In number theory, a multiplicative partition or unordered factorization of an integer n that is greater than 1 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. The number n is itself considered one...
  
   
• Noncrossing partition
  Noncrossing partition
  In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of its application to the theory of free probability...
  
   
• Ordered partition of a set
  Ordered partition of a set
  In combinatorial mathematics, an ordered partition O of a set S is a sequenceof subsets of S, with union is S, which are non-empty, and pairwise disjoint...
  
   
• Partition function (number theory) 
• Partition function (quantum field theory)
  Partition function (quantum field theory)
  In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral:...
  
   
• Partition function (statistical mechanics)
  Partition function (statistical mechanics)
  Partition functions describe the statistical properties of a system in thermodynamic equilibrium. It is a function of temperature and other parameters, such as the volume enclosing a gas...
  
   
  • Derivation of the partition function 
• Partition of an interval
  Partition of an interval
  In mathematics, a partition, P of an interval [a, b] on the real line is a finite sequence of the formIn mathematics, a partition, P of an interval [a, b] on the real line is a finite sequence of the form...
  
   
• Partition of a number 
• Partition of a set
  Partition of a set
  In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...
  
   
  • Ordered partition 
  • Partition refinement
    Partition refinement
    In the design of algorithms, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by splitting its sets into a larger number of smaller sets. In that sense it is dual to the union-find data structure, which also...
    
    
  • Disjoint-set data structure
    Disjoint-set data structure
    In computing, a disjoint-set data structure is a data structure that keeps track of a set of elements partitioned into a number of disjoint subsets. A union-find algorithm is an algorithm that performs two useful operations on such a data structure:* Find: Determine which set a particular element...
    
    
• Partition problem
  Partition problem
  In computer science, the partition problem is an NP-complete problem. The problem is to decide whether a given multiset of integers can be partitioned into two "halves" that have the same sum...
  
   
  • 3-partition problem
    3-partition problem
    The 3-partition problem is an NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triples that all have the same sum...
    
     
• Partition of unity 
• Partition topology
  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...
  
   
• Pentagonal number theorem 
• Plane partition 
• Recursive partitioning
  Recursive partitioning
  Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population based on several dichotomous dependent variables....
  
   
• Stirling number
  Stirling number
  In mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second...
  
   
  • Stirling transform 
• Stratification (mathematics)
  Stratification (mathematics)
  -In mathematical logic:In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing that a unique formal interpretation of a logical theory exists...
  
   
• Tverberg partition 
• Twelvefold way
  Twelvefold way
  In combinatorics, the twelvefold way is a name given to a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number...
  
   
• Young tableau
  Young tableau
  In mathematics, a Young tableau is a combinatorial object useful in representation theory. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tableaux were introduced by Alfred Young, a mathematician at...
  
   
• Young's lattice
  Young's lattice
  In mathematics, Young's lattice is a partially ordered set and a lattice that is formed by all integer partitions. It is named after Alfred Young, who in a series of papers On quantitative substitutional analysis developed representation theory of the symmetric group...