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SUMMARY:Isaac Rajagopal (MIT)
DTSTART:20260716T180000Z
DTEND:20260716T182500Z
DTSTAMP:20260710T111746Z
UID:CANT2026/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/51/
 ">Possible sizes of sumsets</a>\nby Isaac Rajagopal (MIT) as part of Combi
 natorial and additive number theory seminar (CANT 2026)\n\nLecture held in
  Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nNath
 anson introduced the range of cardinalities of $h$-fold sumsets $ \\mathca
 l{R}(h\,k):= \\{|hA|:A \\subseteq \\mathbb{Z} \\text{ and }|A| = k\\}. $ F
 ollowing a remark of Erdös and Szemerédi that determined the form of $\\
 mathcal{R}(h\,k)$ when $h=2$\, Nathanson asked what the form of $\\mathcal
 {R}(h\,k)$ is for arbitrary $h\, k \\in \\mathbb{N}$. For $h \\in \\mathbb
 {N}$\, we prove there is some constant $k_h \\in \\mathbb{N}$ such that if
  $k > k_h$\, then $\\mathcal{R}(h\,k)$ is the entire interval $\\left[hk-h
 +1\,\\binom{h+k-1}{h}\\right]$ except for a specified set of $\\binom{h-1}
 {2}$ numbers. Moreover\, we show that one can take $k_3 = 2$.\n
LOCATION:https://researchseminars.org/talk/CANT2026/51/
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