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SUMMARY:Yoshiharu Kohayakawa (University of São Paulo\, Brazil)
DTSTART:20250520T160000Z
DTEND:20250520T162500Z
DTSTAMP:20260423T041811Z
UID:CANT2025/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/16/
 ">Arithmetic progressions in subsetsums of sparse random sets of integers<
 /a>\nby Yoshiharu Kohayakawa (University of São Paulo\, Brazil) as part o
 f Combinatorial and additive number theory (CANT 2025)\n\nLecture held in 
 CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nGiven a se
 t $S\\subset\\mathbb{N}$\, its sumset $S+S$ is the set of all\nsums $s+s'$
  with both $s$ and $s'$ elements of $S$.  Given\n$p \\colon \\mathbb{N}\\t
 o [0\,1]$\, let $A_n=[n]_p$ be the $p$-random\nsubset of $[n]=\\{1\,\\dots
 \,n\\}$: the random set obtained by including\neach element of $[n]$ in $A
 _n$ independently with probability $p(n)$.\nLet $\\varepsilon>0$ be fixed\
 , and suppose\n$p(n)\\geq n^{-1/2+\\varepsilon}$ for all large enough $n$.
   We prove\nthat\, then\, with high probability\, long arithmetic progress
 ions exist\nin the sumset of any positive density subset of $A_n$\, that i
 s\, with\nprobability approaching $1$ as $n\\to\\infty$\, for any subset $
 S$\nof $A_n$ with a fixed proportion of the elements of $A_n$\, the sumset
 \n$S+S$ contains arithmetic progressions with\n$2^{\\Omega(\\sqrt{\\log n}
 )}$ elements.  \nJoint work with Marcelo Campos and Gabriel Dahia.\n
LOCATION:https://researchseminars.org/talk/CANT2025/16/
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