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Sang June Lee (이상준), On strong Sidon sets of integers

Wednesday, May 8, 2019 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)


Sang June Lee (이상준)
Department of Mathematics, Duksung Women's University

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:

For 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 $x<y\leq z<w$.

The 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 $\mathbb N$.

In 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.


Wednesday, May 8, 2019
4:30 PM - 5:30 PM KST
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Room B232
IBS (기초과학연구원)


Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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