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Permutation polynomial

In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g ( x ) {\displaystyle x\mapsto g(x)} is a bijection. In case the ring is a finite field, the Dickson polynomials, which are closely related to the Chebyshev polynomials, provide examples. Over a finite…

Single variable permutation polynomials over finite fields, Geometric examples & Quadratic permutation polynomials (QPP) over finite rings

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Single variable permutation polynomials over finite fields

CharacteristicSurjectiveInjectiveHermiteIf and only if
16 related topics

Geometric examples

Finite geometryOvalProjective planeO-polynomial
4 related topics

Quadratic permutation polynomials (QPP) over finite rings

Finite ringTurbo codes3GPP Long Term EvolutionPrime number
4 related topics

Schur's conjecture

Algebraic number fieldRing of integersPrime idealsSchur
4 related topics

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Single variable permutation polynomials over finite fields

Geometric examples

Computational complexity

Quadratic permutation polynomials (QPP) over finite rings

Higher degree polynomials over finite rings

Schur's conjecture

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Permutation polynomial

Nodes48
Edges47
Triples81
Avg. degree1.96
Density0.041667
Components1

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Permutation polynomial

Top relations

related to References · 40
Permutation polynomial → Cambridge University Press, Chapter, CRC Press, Daniel, Dickson, Dover, Elements, Encyclopedia, Exposition, Field, Finite, Finite Field Permute, Finite Fields, Galois Field Theory, Gary, Handbook, Harald, II, ISBN, Its Applications
related to Schur's conjecture · 11
Permutation polynomial → Correct, Dickson, Fried, In, Let, Müller, R/P, Schur, Schur's, The, Turnwald
related to Quadratic permutation polynomials (QPP) over finite rings · 6
Permutation polynomial → Actually, For, Long Term Evolution, That, The, Z/nZ
related to Small degree · 6
Permutation polynomial → Dickson, Hermite's, However, Shallue, These, Wanless
related to Some classes of permutation polynomials · 5
Permutation polynomial → Beyond, Dickson, Dn, GF, If
related to Single variable permutation polynomials over finite fields · 4
Permutation polynomial → Due, Fq, GF, Let Fq
related to Exceptional polynomials · 3
Permutation polynomial → An, Fq, GF
related to Geometric examples · 3
Permutation polynomial → GF, In, PG
related to Higher degree polynomials over finite rings · 2
Permutation polynomial → Z/pkZ, Z/pZ
related to Computational complexity · 1
Permutation polynomial → The

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Important terminology

permutation polynomial displaystyle finite polynomials gf field ring dickson degree defines fields fq consider elements prime one linear given quadratic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Permutation polynomialrelated to Computational complexityThe0.60section
Permutation polynomialrelated to Exceptional polynomialsAn0.60section
Permutation polynomialrelated to Exceptional polynomialsGF0.60section
Permutation polynomialrelated to Exceptional polynomialsFq0.60section
Permutation polynomialrelated to Geometric examplesIn0.60section
Permutation polynomialrelated to Geometric examplesPG0.60section
Permutation polynomialrelated to Geometric examplesGF0.60section
Permutation polynomialrelated to Higher degree polynomials over finite ringsZ/pkZ0.60section
Permutation polynomialrelated to Higher degree polynomials over finite ringsZ/pZ0.60section
Permutation polynomialrelated to Quadratic permutation polynomials (QPP) over finite ringsFor0.60section
Permutation polynomialrelated to Quadratic permutation polynomials (QPP) over finite ringsZ/nZ0.60section
Permutation polynomialrelated to Quadratic permutation polynomials (QPP) over finite ringsActually0.60section

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