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SUMMARY:Anne de Roton (Universit\\'e de Lorraine\, Institut Elie Cartan)
DTSTART:20250522T140000Z
DTEND:20250522T142500Z
DTSTAMP:20260423T024836Z
UID:CANT2025/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/39/
 ">Iterated sums races</a>\nby Anne de Roton (Universit\\'e de Lorraine\, I
 nstitut Elie Cartan) as part of Combinatorial and additive number theory (
 CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th f
 loor).\n\nAbstract\nThis is joint work with Paul P\\' eringuey. \\\\\nOur 
 work provides a solution to a question posed by M. Nathanson in late 2024\
 , but we later realized that this problem\, along with an even more challe
 nging one\, had already been solved by N. Kravitz in a paper posted on arX
 iv in January 2025. While our construction is similar to his\, it is simpl
 er\, and we hope that it can serve as an introductory step toward understa
 nding the underlying ideas. \\\\\nNathanson's question is as follows: \\\\
 \n\\textit{For every integer $m \\geq 3$\, do there exist finite sets $A$ 
 and $B$ of integers and an increasing sequence of positive integers $h_1 <
  h_2 < \\cdots < h_m$\, such that: \\\\\n$$ |h_i A| > |h_i B| \\quad \\tex
 t{if } i \\text{ is odd\,} $$\n$$ |h_i A| < |h_i B| \\quad \\text{if } i \
 \text{ is even.} $$ \\\\\nAdditionally\, do there exist such sets with $|A
 | = |B|$? Can such sets be constructed with $|A| = |B|$ and $\\text{diam}(
 A) = \\text{diam}(B)$?} \\\\\nWe provide a positive answer to these questi
 ons and propose an iterative construction of sets that satisfy these condi
 tions.\n
LOCATION:https://researchseminars.org/talk/CANT2025/39/
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