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DTSTART;TZID=Asia/Seoul:20190508T163000
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SUMMARY:Sang June Lee (이상준)\, On strong Sidon sets of integers
DESCRIPTION:Let $\mathbb N$ be the set of natural numbers. A set $A\subset \mathbb N$ is called a Sidon set if the sums $a_1+a_2$\, with $a_1\,a_2\in S$ and $a_1\leq a_2$\, are distinct\, or equivalently\, if \[|(x+w)-(y+z)|\geq 1\] for every $x\,y\,z\,w\in S$ with $x<y\leq z<w$. We define strong Sidon sets as follows: \nFor a constant $\alpha$ with $0\leq \alpha<1$\, a set $S\subset \mathbb N$ is called an $\alpha$-strong Sidon set if \[|(x+w)-(y+z)|\geq w^\alpha\] for every $x\,y\,z\,w\in S$ with $x<y\leq z<w$. \nThe motivation of strong Sidon sets is that a strong Sidon set generates many Sidon sets by altering each element a bit. This infers that a dense strong Sidon set will guarantee a dense Sidon set contained in a sparse random subset of $\mathbb N$. \nIn this talk\, we are interested in how dense a strong Sidon set can be. This is joint work with Yoshiharu Kohayakawa\, Carlos Gustavo Moreira and Vojtěch Rödl.
URL:https://dimag.ibs.re.kr/event/2019-05-08/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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