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SUMMARY:Javier Santiago (University of Puerto Rico)
DTSTART:20200604T203000Z
DTEND:20200604T205500Z
DTSTAMP:20260423T011321Z
UID:CANT2020/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/56/
 ">On permutation binomials of index $q^{e-1}+q^{e-2}+\\cdots+1$</a>\nby Ja
 vier Santiago (University of Puerto Rico) as part of Combinatorial and add
 itive number theory (CANT 2021)\n\n\nAbstract\nThe permutation binomial $f
 (x) = x^r(x^{q-1} + A)$ was studied by K. Li\, L. Qu\, and X. Chen \nover 
 $\\mathbb{F}_{q^2}$. They found that for $1 \\leq r \\leq q+1$\, $f(x)$ is
  a permutation binomial \nif and only if $r = 1$. Over the finite field $\
 \mathbb{F}_{q^3}$ of odd characteristic\, X. Liu obtained \nan analogous r
 esult\, in which for $1 \\leq r \\leq q^2+q+1$\, $f(x)$ permutes $\\mathbb
 {F}_{q^3}$ \nif and only if $r = 1$. In this investigation\, we complete t
 he characterization for $f(x)$ \nover both $\\mathbb{F}_{q^2}$ and $\\math
 bb{F}_{q^3}$\, as well as obtain a complete characterization \nover $\\mat
 hbb{F}_{q^4}$. Furthermore\, for  $e \\geq 5$\, we present some partial re
 sults which narrow \ndown considerably the search for $r's$ that do indeed
  yield permutation binomials of the form \n$f(x) = x^r(x^{q-1} + A)$ over 
 $\\mathbb{F}_{q^e}$.\n\nJoint work with Ariane Masuda and  Ivelisse Rubio.
 \n
LOCATION:https://researchseminars.org/talk/CANT2020/56/
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