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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)

Speaker

Sang June Lee (이상준)
Department of Mathematics, Duksung Women's University
https://sites.google.com/site/sjlee242/

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.

Details

Date:
Wednesday, May 8, 2019
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
View Organizer Website
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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