List of permutation topics - AbsoluteAstronomy.com

This is a list of topics on mathematical permutation

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

Alternating group
Alternating permutation
Antisymmetrizer
Automorphisms of the symmetric and alternating groups
Bijection
Bijection
A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements...
Bit-reversal permutation
Bit-reversal permutation
In applied mathematics, a bit-reversal permutation is a permutation of a sequence with n = 2m elements, defined by reversing the binary digits of the index of each element...
Block (permutation group theory)
Burnside ring
Burnside ring
In mathematics, the Burnside ring of a finite group is an algebraic construction that encodes the different ways the group can act on finite sets...
Cayley's theorem
Cayley's theorem
In group theory, Cayley's theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G...
Circular shift
Circular shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation...
Claw-free permutation
Claw-free permutation
In mathematical and computer science field of cryptography, a group of three numbers is said to be a claw of two permutations f0 and f1 if...
Combination
Combination
In mathematics a combination is a way of selecting several things out of a larger group, where order does not matter. In smaller cases it is possible to count the number of combinations...
Costas array
Costas array
In mathematics, a Costas array can be regarded geometrically as a set of n points lying on the squares of a n×n checkerboard, such that each row or column contains only one point, and that all of the n/2 displacement vectors between each pair of dots are distinct...
Cycle index
Cycle index
In mathematics, and in particular in the field of combinatorics, cycle indices are used in combinatorial enumeration when symmetries are to be taken into account...
Cycle (mathematics)
Cycle (mathematics)
In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing all other elements...
Cycle notation
Cycle notation
In combinatorial mathematics, the cycle notation is a useful convention for writing down a permutation in terms of its constituent cycles. This is also called circular notation and the permutation called a cyclic or circular permutation....
Cycles and fixed points
Cyclic order
Cyclic permutation
Cyclic permutation
A cyclic permutation or circular permutation is a permutation built from one or more sets of elements in cyclic order.The notion "cyclic permutation" is used in different, but related ways:- Definition 1 :right|mapping of permutation...
Derangement
Derangement
In combinatorial mathematics, a derangement is a permutation of the elements of a set such that none of the elements appear in their original position....
Direct sum of permutations
Direct sum of permutations
In combinatorial mathematics, the direct sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by...
Enumerations of specific permutation classes
Enumerations of specific permutation classes
In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively few basis elements.- Classes avoiding one pattern of length 3 :...
Even and odd permutations—see Parity of a permutation
Ewens' sampling formula
Factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
- Falling factorial
Faro shuffle
Faro shuffle
The faro shuffle is a method of shuffling playing cards.In a perfect shuffle or perfect faro shuffle, the deck is split into equal halves of 26 cards which are then pushed together in a certain way so as to make them perfectly interweave....
Fifteen puzzle
Fisher–Yates shuffle
Frobenius group
Frobenius group
In mathematics, a Frobenius group is a transitive permutation group on a finite set, such that no non-trivial elementfixes more than one point and some non-trivial element fixes a point.They are named after F. G. Frobenius.- Structure :...
Generalized permutation matrix
Generalized permutation matrix
In mathematics, a generalized permutation matrix is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero...
Golomb–Dickman constant
Identical particles
Identical particles
Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include elementary particles such as electrons, and, with some clauses, composite particles such as atoms and molecules.There are two...
Inversion (discrete mathematics)
Josephus permutation
Jucys–Murphy element
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...
Levi-Civita symbol
Levi-Civita symbol
The Levi-Civita symbol, also called the permutation symbol, antisymmetric symbol, or alternating symbol, is a mathematical symbol used in particular in tensor calculus...
Major index
Ménage problem
Ménage problem
In combinatorial mathematics, the ménage problem or problème des ménages asks for the number of different ways in which it is possible to seat a set of heterosexual couples at a dining table so that men and women alternate and nobody sits next to his or her partner...
Method ringing
Method ringing
Method ringing is a form of change ringing...
Oligomorphic group
Oligomorphic group
In group theory, a branch of mathematics, an oligomorphic group is a particular kind of permutation group. If a group G acts on a set S, then G is said to be oligomorphic if every Cartesian product, Sn of S has finitely many orbits under the action of G...
Order statistic
Order statistic
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference....
Parity of a permutation
Parker vector
Parker vector
In mathematics, especially the field of group theory, the Parker vector is an integer vector that describes a permutation group in terms of the cycle structure of its elements.-Definition:...
Permutable prime
Permutable prime
A permutable prime is a prime number, which, in a given base, can have its digits' positions switched through any permutation and still spell a prime number. H. E...
Permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
Permutation automaton
Permutation automaton
In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states....
Permutation cipher
Permutation cipher
In classical cryptography, a permutation cipher is a transposition cipher in which the key is a permutation.To apply a cipher, a random permutation of size e is generated...
Permutation (music)
Permutation (music)
In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...
Permutation graph
Permutation graph
In areas of mathematics influenced by graph theory, a permutation graph is the intersection graph of a family of line segments that connect two parallel lines in the Euclidean plane...
Permutation group
Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...
Permutation matrix
Permutation matrix
In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere...
- Generalized permutation matrix
  Generalized permutation matrix
  In mathematics, a generalized permutation matrix is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero...
Permutation pattern
Permutation pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. The permutation π, written as a word in one-line notation , is said to contain the permutation σ if there exists a subsequence of entries of π that has the same...
Permutation polynomial
Permutation polynomial
In mathematics, a permutation polynomial is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x \mapsto g is one-to-one...
Permutohedron
Permutohedron
In mathematics, the permutohedron of order n is an -dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector .-History:According to , permutohedra were first studied by...
Primitive permutation group
Primitive permutation group
In mathematics, a permutation group G acting on a set X is called primitive if G acts transitively on X and G preserves no nontrivial partition of X...
Random permutation
Random permutation
A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation...
Random permutation statistics
Random permutation statistics
The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect to select a random...
Rank 3 permutation group
Rank 3 permutation group
In mathematical finite group theory, a rank 3 permutation group is a group acting transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by...
Rankit
Rankit
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.-Example:This is perhaps most...
Representation theory of the symmetric group
Representation theory of the symmetric group
In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained. This has a large area of potential applications, from symmetric function theory to problems of quantum...
Rencontres numbers
Resampling (statistics)
Resampling (statistics)
In statistics, resampling is any of a variety of methods for doing one of the following:# Estimating the precision of sample statistics by using subsets of available data or drawing randomly with replacement from a set of data points # Exchanging labels on data points when performing significance...
Robinson–Schensted correspondence
Schreier vector
Schreier vector
In mathematics, especially the field of computational group theory, a Schreier vector is a tool for reducing the time and space complexity required to calculate orbits of a permutation group.-Overview:...
Separable permutation
Separable permutation
In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations can also be characterized as the permutations that contain neither 2413 nor 3142...
Shuffling
Skew sum of permutations
Skew sum of permutations
In combinatorial mathematics, the skew sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by...
Sorting algorithm
Sorting algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order...
Sorting network
Sorting network
A sorting network is an abstract mathematical model of a network of wires and comparator modules that is used to sort a sequence of numbers. Each comparator connects two wires and sorts the values by outputting the smaller value to one wire, and the larger to the other...
Stanley–Wilf conjecture
Steinhaus–Johnson–Trotter algorithm
Strong generating set
Strong generating set
In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a stabilizer chain...
Substitution cipher
Substitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
Substitution-permutation network
Substitution-permutation network
In cryptography, an SP-network, or substitution-permutation network , is a series of linked mathematical operations used in block cipher algorithms such as AES .Other ciphers that use SPNs are 3-Way, SAFER, SHARK, and Square....
Sum of permutations:
- Direct sum of permutations
  Direct sum of permutations
  In combinatorial mathematics, the direct sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by...
- Skew sum of permutations
  Skew sum of permutations
  In combinatorial mathematics, the skew sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by...
Superpattern
Superpattern
In mathematics , k-superpattern is a permutation of minimal length that contains all permutation patterns of length k.-Examples :...
Symmetric function
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
Symmetric group
Symmetric group
In mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself...
Symmetric inverse semigroup
Szymanski's conjecture
Szymanski's conjecture
In mathematics, Szymanski's conjecture, named after , states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths...
Transposition cipher
Transposition cipher
In cryptography, a transposition cipher is a method of encryption by which the positions held by units of plaintext are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed...
Transposition (mathematics)
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...
Weak order of permutations
Wreath product
Wreath product
In mathematics, the wreath product of group theory is a specialized product of two groups, based on a semidirect product. Wreath products are an important tool in the classification of permutation groups and also provide a way of constructing interesting examples of groups.Given two groups A and H...
Young symmetrizer
Young symmetrizer
In mathematics, a Young symmetrizer is an element of the group algebra of the symmetric group, constructed in such a way that the image of the element corresponds to an irreducible representation of the symmetric group over the complex numbers. A similar construction works over any field, and the...
Zassenhaus group
Zassenhaus group
In mathematics, a Zassenhaus group, named after Hans Julius Zassenhaus, is a certain sort of doubly transitive permutation group very closely related to rank-1 groups of Lie type.- Definition :...
Zolotarev's lemma
Zolotarev's lemma
In number theory, Zolotarev's lemma states that the Legendre symbol\leftfor an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation:...

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