Explicit determination of a class of permutation rational functions in any characteristic
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916003781279744 |
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| author | Li, Yi Tang, Deng |
| author_facet | Li, Yi Tang, Deng |
| contents | In this paper, we make use of the classification results of low-degree permutation rational functions together with their geometric properties to investigate rational functions that induce permutations on the multiplicative subgroup mu_q+1, where q is a prime power. By carefully analyzing the structural conditions under which such rational functions permute muq+1, we obtain an explicit description of a broad class of permutation rational functions of small degree. As a direct application of these findings, we explicitly determine many permutation quadrinomials over Fq2 that are induced by degree-3 rational functions permuting muq+1. Our approach not only unifies and extends several existing results in the literature but also provides a concrete geometric perspective for characterizing permutation polynomials over Fq2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit determination of a class of permutation rational functions in any characteristic Li, Yi Tang, Deng Number Theory Information Theory Combinatorics In this paper, we make use of the classification results of low-degree permutation rational functions together with their geometric properties to investigate rational functions that induce permutations on the multiplicative subgroup mu_q+1, where q is a prime power. By carefully analyzing the structural conditions under which such rational functions permute muq+1, we obtain an explicit description of a broad class of permutation rational functions of small degree. As a direct application of these findings, we explicitly determine many permutation quadrinomials over Fq2 that are induced by degree-3 rational functions permuting muq+1. Our approach not only unifies and extends several existing results in the literature but also provides a concrete geometric perspective for characterizing permutation polynomials over Fq2. |
| title | Explicit determination of a class of permutation rational functions in any characteristic |
| topic | Number Theory Information Theory Combinatorics |
| url | https://arxiv.org/abs/2605.11528 |