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- Parity_of_a_permutation abstract "In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective mappings from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation of X can be defined as the parity of the number of inversions for σ, i.e., of pairs of elements x, y of X such that and .The sign or signature of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd. The signature defines the alternating character of the symmetric group Sn. Another notation for the sign of a permutation is given by the more general Levi-Civita symbol , which is defined for all maps from X to X, and has value zero for non-bijective maps.The sign of a permutation can be explicitly expressed assgn(σ) = (−1)N(σ)where N(σ) is the number of inversions in σ. Alternatively, the sign of a permutation σ can be defined from its decomposition into the product of transpositions assgn(σ) = (−1)mwhere m is the number of transpositions in the decomposition. Although such a decomposition is not unique, the parity of the number of transpositions in all decompositions is the same, implying that the sign of a permutation is well-defined.".
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- Parity_of_a_permutation wikiPageExternalLink 1000px-Symmetric_group_4%3B_permutation_list_with_matrices.svg.png.
- Parity_of_a_permutation wikiPageID "49727".
- Parity_of_a_permutation wikiPageRevisionID "586941821".
- Parity_of_a_permutation hasPhotoCollection Parity_of_a_permutation.
- Parity_of_a_permutation title "Even Permutation".
- Parity_of_a_permutation urlname "EvenPermutation".
- Parity_of_a_permutation subject Category:Articles_containing_proofs.
- Parity_of_a_permutation subject Category:Group_theory.
- Parity_of_a_permutation subject Category:Parity.
- Parity_of_a_permutation subject Category:Permutations.
- Parity_of_a_permutation type Abstraction100002137.
- Parity_of_a_permutation type Change107296428.
- Parity_of_a_permutation type Event100029378.
- Parity_of_a_permutation type Happening107283608.
- Parity_of_a_permutation type Permutations.
- Parity_of_a_permutation type PsychologicalFeature100023100.
- Parity_of_a_permutation type Substitution107443761.
- Parity_of_a_permutation type Variation107337390.
- Parity_of_a_permutation type YagoPermanentlyLocatedEntity.
- Parity_of_a_permutation comment "In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective mappings from X to X) fall into two classes of equal size: the even permutations and the odd permutations.".
- Parity_of_a_permutation label "Paridade de uma permutação".
- Parity_of_a_permutation label "Parity of a permutation".
- Parity_of_a_permutation label "Signature d'une permutation".
- Parity_of_a_permutation label "Vorzeichen (Permutation)".
- Parity_of_a_permutation label "置换的奇偶性".
- Parity_of_a_permutation sameAs Znaménko_permutace.
- Parity_of_a_permutation sameAs Vorzeichen_(Permutation).
- Parity_of_a_permutation sameAs Signature_d'une_permutation.
- Parity_of_a_permutation sameAs Paridade_de_uma_permutação.
- Parity_of_a_permutation sameAs m.0d6l9.
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- Parity_of_a_permutation depiction Symmetric_group_4;_permutation_list_with_matrices.svg.
- Parity_of_a_permutation isPrimaryTopicOf Parity_of_a_permutation.