Permutation binomials
A polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1. Even in this restricted setting, it is impossible to give general necessary and sufficient con...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000497 |
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| _version_ | 1832562528925777920 |
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| author | Charles Small |
| author_facet | Charles Small |
| author_sort | Charles Small |
| collection | DOAJ |
| description | A polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known. |
| format | Article |
| id | doaj-art-4e96a219428749d4a826b96eee86b31e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4e96a219428749d4a826b96eee86b31e2025-02-03T01:22:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113233734210.1155/S0161171290000497Permutation binomialsCharles Small0Department of Mathematics and Statistics, Queen's University, Ontario, Kingston K7L 3N6, CanadaA polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known.http://dx.doi.org/10.1155/S0161171290000497permutation polynomialsfinite fieldsbinomials. |
| spellingShingle | Charles Small Permutation binomials International Journal of Mathematics and Mathematical Sciences permutation polynomials finite fields binomials. |
| title | Permutation binomials |
| title_full | Permutation binomials |
| title_fullStr | Permutation binomials |
| title_full_unstemmed | Permutation binomials |
| title_short | Permutation binomials |
| title_sort | permutation binomials |
| topic | permutation polynomials finite fields binomials. |
| url | http://dx.doi.org/10.1155/S0161171290000497 |
| work_keys_str_mv | AT charlessmall permutationbinomials |