A generalized Lucas sequence and permutation binomials

DOI10.1090/S0002-9939-05-08220-1zbMath1137.11355OpenAlexW1641456849MaRDI QIDQ5695738

Qiang Wang, Amir Akbary

Publication date: 6 October 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-08220-1

zbMATH Keywords

permutation polynomialgeneralized Lucas sequenceHermite criterionpermutation binomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

Further results on complete permutation monomials over finite fields ⋮ The generalized order-\(k\) Lucas sequences in finite groups ⋮ Generalized Lucas polynomials over finite fields ⋮ Specific permutation polynomials over finite fields ⋮ Cyclotomy and permutation polynomials of large indices ⋮ Permutation polynomials over finite fields from a powerful lemma ⋮ On polynomials of the form \(x^{r}f(x^{(q - 1)/l})\) ⋮ ON SOME CLASSES OF PERMUTATION POLYNOMIALS ⋮ Determination of a type of permutation binomials over finite fields ⋮ Complete permutation polynomials over finite fields of odd characteristic ⋮ Cyclotomic Mapping Permutation Polynomials over Finite Fields ⋮ Permutation polynomials over finite fields -- a survey of recent advances ⋮ A class of permutation binomials over finite fields ⋮ On inverse permutation polynomials ⋮ On some permutation polynomials over $\mathbb {F}_q$ of the form $x^r h(x^{(q-1)/d})$ ⋮ Permutation binomials over finite fields

Uses Software

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Cites Work

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• Schur covers and Carlitz's conjecture
• Factorization properties of Chebyshev polynomials
• Permutation polynomials of the form \(x^r f(x^{(q-1)/d)}\) and their group structure
• A geometric approach to permutation polynomials over a finite field