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

May 8 Wednesday @ 4:30 PM - 5:30 PM

Room B232, IBS (기초과학연구원)

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.


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


Sang-il Oum
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
Discrete Mathematics Group (DIMAG)
Pioneer Research Center for Mathematical and Computational Sciences
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr
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