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SUMMARY:Vivekanand Goswami (Indian Institute of Technology Bhilai\, India)
DTSTART:20260717T123000Z
DTEND:20260717T125500Z
DTSTAMP:20260805T021040Z
UID:CANT2026/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/58/
 ">Restricted set addition in finite abelian groups</a>\nby Vivekanand Gosw
 ami (Indian Institute of Technology Bhilai\, India) as part of Combinatori
 al and additive number theory seminar (CANT 2026)\n\nLecture held in Scien
 ce Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $A$ be
  a nonempty subset of a finite abelian group $G$ of order $n$. For an inte
 ger $h \\geq 2$\, the restricted $h$-fold sumset $h^\\wedge A$ is the set 
 of all sums of $h$ distinct elements of $A$. It is known that if $G$ is a 
 group of order $n$ and $A$ is a subset of $G$ such that $|A| > \\frac{n}{2
 }$\, then $h^{\\wedge}A = G$ under some conditions on $h$ and $n$. While t
 he constant $1/2$ is optimal for groups of even order\, it is not optimal 
 for groups of odd order. For an integer $h \\geq 4$\, let $\\alpha_h$ be t
 he unique positive root of the polynomial $3^{h - 2} x^{h - 1} + x - 1$. I
 n this talk\, we discuss that for any $\\alpha > \\alpha_h$\, there exists
  a positive integer $M_h(\\alpha)$\, which is determined precisely\, such 
 that for all $n > M_h(\\alpha)$ with $n$ odd\, if $A$ is a subset of a fin
 ite abelian group $G$ of order $n$ and if $|A| \\geq \\alpha n$\, then $h^
 {\\wedge} A = G$. Moreover\, $\\alpha_h > \\alpha_{h + 1}$ for $h \\geq 4$
  and $\\alpha_h$ approaches $\\frac{1}{3}$ as $h$ increases\, and the cons
 tant $\\frac{1}{3}$ is optimal when the smallest prime dividing $n$ is $3$
 .\n
LOCATION:https://researchseminars.org/talk/CANT2026/58/
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