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SUMMARY:Ariane Masuda (New York City College of Technology\, CUNY)
DTSTART:20220526T203000Z
DTEND:20220526T205500Z
DTSTAMP:20260423T011340Z
UID:CANT2022/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/44/
 ">Redei permutations with the same cycle structure</a>\nby Ariane Masuda (
 New York City College of Technology\, CUNY) as part of Combinatorial and a
 dditive number theory (CANT 2022)\n\n\nAbstract\nPermutation polynomials o
 ver finite fields have been extensively studied over the past decades. Amo
 ng the major challenges in this area are the questions concerning their cy
 cle structures as they capture relevant properties\, both theoretically an
 d practically. In this talk we focus on a family of permutation polynomial
 s\, the so called R\\'edei permutations. Although their cycle structures a
 re known\, there are other related questions that can be investigated. For
  example\, when do two R\\'edei permutations have the same cycle structure
 ? We give a characterization of such pairs\, and present explicit families
  of R\\'edei permutations with the same cycle structure. We also discuss s
 ome results regarding R\\'edei permutations with a particularly simple cyc
 le structure\, consisting of $1$- and $j$-cycles only\, when $j$ is $4$ or
  a prime number. The case $j = 2$ is specially important in some applicati
 ons. We completely describe R\\'edei involutions with a prescribed cycle s
 tructure\, and show that the only R\\'edei permutations with a unique cycl
 e structure are the involutions. \n\nThis is joint work with Juliane Capav
 erde and Virg\\'inia Rodrigues.\n
LOCATION:https://researchseminars.org/talk/CANT2022/44/
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