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SUMMARY:Vivekanand Goswami (Indian Institute of Technology Gandhinagar\, I
 ndia)
DTSTART:20260717T123000Z
DTEND:20260717T125500Z
DTSTAMP:20260710T111745Z
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 Gandhinagar\, India) as part of Combin
 atorial and additive number theory seminar (CANT 2026)\n\nLecture held in 
 Science 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
  integer $h \\geq 2$\, 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 $n$. Wh
 ile the constant $1/2$ is optimal for groups of even order\, it is not opt
 imal for groups of odd order. For an integer $h \\geq 4$\, let $\\alpha_h$
  be the unique positive root of the polynomial $3^{h - 2} x^{h - 1} + x - 
 1$. In this talk\, we discuss that for any $\\alpha > \\alpha_h$\, there e
 xists 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 finite abelian group $G$ of order $n$ and if $|A| \\geq \\alpha n$\, the
 n $h^{\\wedge} A = G$. Moreover\, $\\alpha_h > \\alpha_{h + 1}$ for $h \\g
 eq 4$ and $\\alpha_h$ approaches $\\frac{1}{3}$ as $h$ increases\, and the
  constant $\\frac{1}{3}$ is optimal when the smallest prime dividing $n$ i
 s $3$.\n
LOCATION:https://researchseminars.org/talk/CANT2026/58/
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