[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j140275

ON SIDON SETS IN A RANDOM SET OF VECTORS

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

Publication Information

Journal of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 503-517 More about this Journal

Abstract

For positive integers d and n, let $$[n$ $]$ $^d$$ be the set of all vectors ( $a_1,a_2,{\cdots},a_d$ ), where ai is an integer with $0{\leq}a_i{\leq}n-1$ . A subset S of $$[n$ $]$ $^d$$ is called a Sidon set if all sums of two (not necessarily distinct) vectors in S are distinct. In this paper, we estimate two numbers related to the maximum size of Sidon sets in $$[n$ $]$ $^d$$ . First, let $\mathcal{Z}_{n,d}$ be the number of all Sidon sets in $$[n$ $]$ $^d$$ . We show that ${\log}(\mathcal{Z}_{n,d})={\Theta}(n^{d/2})$ , where the constants of ${\Theta}$ depend only on d. Next, we estimate the maximum size of Sidon sets contained in a random set $$[n$ $]$ $^d_p$$ , where $$[n$ $]$ $^d_p$$ denotes a random set obtained from $$[n$ $]$ $^d$$ by choosing each element independently with probability p.

Keywords

Sidon set; Sidon sequence; vector;

Citations & Related Records

Reference

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