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SUMMARY:Paolo Leonetti (Universita Bocconi\, Italy)
DTSTART:20200602T130000Z
DTEND:20200602T132500Z
DTSTAMP:20260423T011320Z
UID:CANT2020/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/15/
 ">On the density of sumsets</a>\nby Paolo Leonetti (Universita Bocconi\, I
 taly) as part of Combinatorial and additive number theory (CANT 2021)\n\n\
 nAbstract\nWe define a large family $\\mathcal{D}$ of partial set function
 s \n$\\mu: \\mathrm{dom}(\\mu) \\subseteq \\mathcal{P}(\\mathbf{N}) \\to \
 \mathbf{R}$ satisfying certain axioms. \nExamples of "densities" $\\mu \\i
 n \\mathcal{D}$ include the asymptotic\, Banach\, logarithmic\, analytic\,
  \nPólya\, and Buck densities. \nWe prove several results on sumsets whic
 h were previously obtained for the asymptotic density. \nFor instance\, we
  show that for each $n \\in \\mathbf N^+$ and $\\alpha \\in [0\,1]$\, ther
 e exists \n$A \\subseteq \\mathbf{N}$ with $kA \\in \\text{dom}(\\mu)$ and
  $\\mu(kA) = \\alpha k/n$ \nfor every $\\mu \\in \\mathcal{D}$ and every $
 k=1\,\\ldots\, n$\, where $kA$ denotes \nthe $k$-fold sumset $A+\\cdots+A$
 . \nJoint work with Salvatore Tringali.\n
LOCATION:https://researchseminars.org/talk/CANT2020/15/
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