Anbar Meidl, Nurdagül
(2022)
*On a special type of permutation rational functions.*
Applicable Algebra in Engineering, Communication and Computing
.
ISSN 0938-1279 (Print) 1432-0622 (Online)
Published Online First http://dx.doi.org/10.1007/s00200-022-00592-1

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Official URL: http://dx.doi.org/10.1007/s00200-022-00592-1

## Abstract

Let p be a prime and n be a positive integer. We consider rational functions
fb(X) = X + 1∕(Xp − X + b) over 픽pn with Tr(b) ≠ 0. In Hou and Sze (Finite Fields
Appl 68, Paper No. 10175, 2020), it is shown that fb(X) is not a permutation for
p > 3 and n ≥ 5, while it is for p = 2, 3 and n ≥ 1. It is conjectured that fb(X) is
also not a permutation for p > 3 and n = 3, 4, which was recently proved sufciently
large primes in Bartoli and Hou (Finite Fields Appl 76, Paper No. 101904, 2021). In
this note, we give a new proof for the fact that fb(X) is not a permutation for p > 3
and n ≥ 5. With this proof, we also show the existence of many elements b ∈ 픽pn for
which fb(X) is not a permutation for n = 3, 4.

Item Type: | Article |
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Uncontrolled Keywords: | Function fields/curves, Permutation polynomials, Rational places/points |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA150-272.5 Algebra |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Nurdagül Anbar Meidl |

Date Deposited: | 09 Feb 2023 14:26 |

Last Modified: | 09 Feb 2023 14:26 |

URI: | https://research.sabanciuniv.edu/id/eprint/45221 |