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SUMMARY:Vincent Schinina (CUNY Graduate Center)
DTSTART:20250522T200000Z
DTEND:20250522T202500Z
DTSTAMP:20260423T005756Z
UID:CANT2025/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/49/
 ">On a missing interval of integers from $\\mathcal{R}_{\\mathbf{Z}}(h\,4)
 $</a>\nby Vincent Schinina (CUNY Graduate Center) as part of Combinatorial
  and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate C
 enter - Science Center (4th floor).\n\nAbstract\nThe set $\\mathcal{R}_{\\
 Z}(h\,4)$ consists of all possible sizes for the $h$-fold sumset of  sets 
 containing four integers. An immediate question to ask is what are the ele
 ments of this set? We know that $\\mathcal{R}_{\\Z}(h\,4)\\subseteq [3h+1\
 ,\\binom{h+3}{h}]$\, where the right side is an interval of integers that 
 includes the endpoints. These endpoints are known to be attained. By obser
 vation\, it appears that the interval of integers $[3h+2\,4h-1]$ is absent
  from $\\mathcal{R}_{\\Z}(h\,4)$. We will briefly discuss the procedure us
 ed to prove that the integers in $[3h+2\,4h-1]$ are not possible sizes for
  the $h$-fold sumset of a set containing four integers. Furthermore\, we w
 ill confirm that this interval can't be made larger by exhibiting a set wh
 ose h-fold sumset has size $4h$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/49/
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