Chebyshev action on finite fields
Given a polynomial ϕ(x) and a finite field Fq one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under ϕ. When ϕ is a Chebyshev polynomial of prime degree, the graphs display an unusual d...
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| Veröffentlicht in: | Discrete mathematics 2014-02, Vol.315-316, p.83-94 |
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| container_title | Discrete mathematics |
| container_volume | 315-316 |
| creator | Alden Gassert, T. |
| description | Given a polynomial ϕ(x) and a finite field Fq one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under ϕ. When ϕ is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry. In this paper we provide a complete description of these graphs, and then use these graphs to determine the decomposition of primes in the Chebyshev radical extensions. |
| doi_str_mv | 10.1016/j.disc.2013.10.014 |
| format | Article |
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| ispartof | Discrete mathematics, 2014-02, Vol.315-316, p.83-94 |
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| language | eng |
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| source | Access via ScienceDirect (Elsevier); EZB-FREE-00999 freely available EZB journals |
| subjects | Chebyshev approximation Chebyshev polynomial Emission Finite field Graph theory Graphs Iterated polynomial Mathematical analysis Polynomials Post-critically finite map Prime decomposition Radicals Symmetry |
| title | Chebyshev action on finite fields |
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