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SUMMARY:Noah Luntzlara (University of Michigan)
DTSTART:20200605T193000Z
DTEND:20200605T195500Z
DTSTAMP:20260423T011157Z
UID:CANT2020/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/68/
 ">Sets arising as minimal additive complements in the integers</a>\nby Noa
 h Luntzlara (University of Michigan) as part of Combinatorial and additive
  number theory (CANT 2021)\n\n\nAbstract\nA subset $C$ of a group $G$ is a
  \\emph{minimal additive complement} to $W \\subseteq G$ \nif $C +W = G$ a
 nd if $C' + W \\neq G$ for any proper subset $C'\\subsetneq C$. \nWork sta
 rted by Nathanson has focused on which sets $W\\subseteq \\mathbb{Z}$ have
  minimal \nadditive complements. We instead investigate which sets $C\\sub
 seteq \\mathbb{Z}$ arise \nas minimal additive complements to some set $W\
 \subseteq \\mathbb{Z}$. \nWe confirm a conjecture of Kwon in showing that 
 bounded below sets containing arbitrarily large \ngaps arise as minimal ad
 ditive complements. We provide partial results for determining which \neve
 ntually periodic sets arise as minimal additive complements. We place boun
 ds on the density \n of sets which arise as minimal additive complements t
 o finite sets\, including periodic sets which \n arise as minimal additive
  complements. We conclude with several conjectures and questions \n concer
 ning the structure of minimal additive complements.\n
LOCATION:https://researchseminars.org/talk/CANT2020/68/
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