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SUMMARY:Ariane Masuda (New York City Tech (CUNY))
DTSTART:20200602T193000Z
DTEND:20200602T195500Z
DTSTAMP:20260423T011223Z
UID:CANT2020/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/26/
 ">Redei permutations with cycles of length $1$ and $p$</a>\nby Ariane Masu
 da (New York City Tech (CUNY)) as part of Combinatorial and additive numbe
 r theory (CANT 2021)\n\n\nAbstract\nLet $\\mathbb F_q$ be the finite field
  of odd characteristic with $q$ elements \nand $\\mathbb P^1(\\mathbb F_q)
 :=\\mathbb F_q\\cup \\{\\infty\\}$. Consider the binomial expansion \n$\\d
 isplaystyle (x+\\sqrt y)^n = N(x\,y)+D(x\,y)\\sqrt{y}.$\nFor $n\\in\\mathb
 b N$ and $a \\in \\mathbb F_q$\, the <i>Rédei function</i>\n$R_{n\,a}\\co
 lon \\mathbb P^1(\\mathbb F_q)  \\to \\mathbb P^1(\\mathbb F_q)$ is define
 d by\n$$\nR_{n\,a}(x)=\n\\begin{cases} \\dfrac{N(x\,a)}{D(x\,a)} & \\text{
  if } D(x\,a)\\neq 0\,  x\\neq\\infty\\\\\n \n\\infty & \\text{ if } D(x\,
 a)=0\, x\\neq\\infty\,  \\text{ or if } x=\\infty.\n\\end{cases}\n$$\nRéd
 ei functions have been used in several applications such as  cryptography 
 and\n coding theory as well as in the generation of pseudorandom numbers a
 nd Pell equations. \n In this talk we will present results on R\\'edei per
 mutations that decompose in cycles \nof length $1$ and $p$\, where $p$ is 
 prime.  In particular\, we will describe \nall Rédei functions that are i
 nvolutions. \n\nJoint work with  Juliane Capaverde and  Virgínia Rodrigue
 s.\n
LOCATION:https://researchseminars.org/talk/CANT2020/26/
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