Discrete Mathematics Group

Sang June Lee (이상준), On strong Sidon sets of integers
2019-05-08 16:30 - 17:30 (Asia/Seoul) | Room B232, IBS (기초과학연구원)
Let $mathbb N$ be the set of natural numbers. A set $Asubset mathbb N$ is called a Sidon set if the sums $a_1+a_2$, with $a_1,a_2in S$ and $a_1leq a_2$, are distinct, or equivalently, if [|(x+w)-(y+z)|geq 1] for every $x,y,z,win S$ with $x<yleq z<w$. We define strong Sidon sets as follows:
For a constant $alpha$ with $0leq alpha<1$, a set $Ssubset mathbb N$ is called an $alpha$-strong Sidon set if [|(x+w)-(y+z)|geq w^alpha] for every $x,y,z,win S$ with $x<yleq z<w$.
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.
