Event
01_1
| 제출번호(No.) | 0011 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Discrete Mathematics (DM) |
| 영문제목 (Title(Eng.)) |
Infinite Sidon sets contained in sparse random sets of integers |
| 저자(Author(s)) |
Y. Kohayakawa1, Sang June Lee2, C. G. Moreira3, V. Rodl4 University of Sao Paulo1, Duksung Women's University2, IMPA, Rio de Janeiro3, Emory University4 |
| 초록본문(Abstract) | A set $S$ of natural numbers is a \emph{Sidon} set if all the sums $s_1+s_2$ with $s_1$, $s_2\in S$ and $s_1\leq s_2$ are distinct. Let constants $\alpha>0$ and $0<\delta<1$ be fixed, and let $p_m=\min\{1,\alpha m^{-1+\delta}\}$ for all positive integers $m$. Generate a random set $R\subset\mathbb N$ by adding $m$ to $R$ with probability $p_m$, independently for each $m$. We investigate how dense a Sidon set $S$ contained in $R$ can be. Our results show that the answer is qualitatively very different in at least three ranges of $\delta$. We prove quite accurate results for the range $0<\delta\leq2/3$, but only obtain partial results for the range $2/3<\delta\leq1$. |
| 분류기호 (MSC number(s)) |
05A16, 11B75 |
| 키워드(Keyword(s)) | Sidon set, Sidon sequence |
| 강연 형태 (Language of Session (Talk)) |
Korean |