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SUMMARY:Sándor Kiss (Budapest University of Technology and Economics\, Hu
 ngary)
DTSTART:20260717T133000Z
DTEND:20260717T135500Z
DTSTAMP:20260710T111745Z
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\, Hungary) as part of Combinato
 rial and additive number theory seminar (CANT 2026)\n\nLecture held in Sci
 ence Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $k\\
 ge 2$ be an integer and let $A$ be a set of nonnegative integers. The repr
 esentation function $R_{A\,k}(n)$ for the set $A$ is the number of represe
 ntations of a nonnegative integer $n$ as the sum of $k$ terms from $A$. A 
 few years ago\, Bell and Shallit constructed a set $A$ of natural numbers 
 such that $\\mathbb{N}\\setminus A$ is infinite\, but the corresponding re
 presentation function is strictly increasing. Later\, together with Csaba 
 Sándor and Yang Quan-Hui\, we improved their result. Furthermore\, we con
 structed a dense set such that the corresponding representation function i
 s not strictly increasing. In my talk I will also give an overview of the 
 recent progress on this topic.\n
LOCATION:https://researchseminars.org/talk/CANT2026/60/
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