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SUMMARY:Sándor Kiss (Budapest University of Technology and Economics\, an
 d HUN-REN Rényi Institute of Mathematics\, Hungary)
DTSTART:20260717T133000Z
DTEND:20260717T135500Z
DTSTAMP:20260805T032329Z
UID:CANT2026/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/60/
 ">Monotone increasing representation functions</a>\nby Sándor Kiss (Budap
 est University of Technology and Economics\, and HUN-REN Rényi Institute 
 of Mathematics\, Hungary) as part of Combinatorial and additive number the
 ory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Grad
 uate Center (4th floor).\n\nAbstract\nLet $k\\ge 2$ be an integer and let 
 $A$ be a set of nonnegative integers. The representation function $R_{A\,k
 }(n)$ for the set $A$ is the number of representations of a nonnegative in
 teger $n$ as the sum of $k$ terms from $A$. A few years ago\, Bell and Sha
 llit constructed a set $A$ of natural numbers such that $\\mathbb{N}\\setm
 inus A$ is infinite\, but the corresponding representation function is str
 ictly increasing. Later\, together with Csaba Sándor and Yang Quan-Hui\, 
 we improved their result. Furthermore\, we constructed a dense set such th
 at the corresponding representation function is not strictly increasing. I
 n my talk I will also give an overview of the recent progress on this topi
 c.\n
LOCATION:https://researchseminars.org/talk/CANT2026/60/
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