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  2. Permutation - Wikipedia

    en.wikipedia.org/wiki/Permutation

    Permutations without repetition on the left, with repetition to their right. If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which each element appears a number of times equal exactly to its multiplicity in M. An anagram of a word having some repeated letters is an example of a multiset ...

  3. Permutation representation - Wikipedia

    en.wikipedia.org/wiki/Permutation_representation

    If is a permutation group of degree , then the permutation representation of is the linear representation of ρ : G → GL n ⁡ ( K ) {\displaystyle \rho \colon G\to \operatorname {GL} _{n}(K)} which maps g ∈ G {\displaystyle g\in G} to the corresponding permutation matrix (here K {\displaystyle K} is an arbitrary field ). [ 2 ]

  4. Permutation matrix - Wikipedia

    en.wikipedia.org/wiki/Permutation_matrix

    Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.

  5. List of permutation topics - Wikipedia

    en.wikipedia.org/wiki/List_of_permutation_topics

    Enumerations of specific permutation classes; Factorial. Falling factorial; Permutation matrix. Generalized permutation matrix; Inversion (discrete mathematics) Major index; Ménage problem; Permutation graph; Permutation pattern; Permutation polynomial; Permutohedron; Rencontres numbers; Robinson–Schensted correspondence; Sum of permutations ...

  6. Levi-Civita symbol - Wikipedia

    en.wikipedia.org/wiki/Levi-Civita_symbol

    Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon ε or ϵ , or less commonly the Latin lower case e .

  7. Permutation pattern - Wikipedia

    en.wikipedia.org/wiki/Permutation_pattern

    In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.

  8. Exchange matrix - Wikipedia

    en.wikipedia.org/wiki/Exchange_matrix

    In mathematics, especially linear algebra, the exchange matrices (also called the reversal matrix, backward identity, or standard involutory permutation) are special cases of permutation matrices, where the 1 elements reside on the antidiagonal and all other elements are zero.

  9. Permutation codes - Wikipedia

    en.wikipedia.org/wiki/Permutation_Codes

    Using a [,,] linear block code, one can prove that there exists a permutation code in the symmetric group of degree , having minimum distance at least and large cardinality. [10] A lower bound for permutation codes that provides asymptotic improvements in certain regimes of length and distance of the permutation code [ 10 ] is discussed below.