Result: Cameron-Erdős Modulo a Prime: Cameron-Erdős modulo a prime
Title:
Cameron-Erdős Modulo a Prime: Cameron-Erdős modulo a prime
Authors:
Source:
Finite Fields and Their Applications. 8:108-119
Publisher Information:
Elsevier BV, 2002.
Publication Year:
2002
Subject Terms:
Algebra and Number Theory, Arithmetic progressions, Applied Mathematics, 0102 computer and information sciences, Cameron-Erdős conjecture, 01 natural sciences, Theoretical Computer Science, sum-free set, Additive number theory, partitions, Algebraic combinatorics, Other combinatorial number theory, 0101 mathematics, Arithmetic and combinatorial problems involving abstract finite groups, Engineering(all), Abelian groups
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1071-5797
DOI:
10.1006/ffta.2001.0330
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....800367cc1e80c5d4f500251a9aea95f8
Database:
OpenAIRE
Further Information
For a subset \({\mathcal A}\subset G\) of an abelian group let \({\text{ SF}}[{\mathcal A}]\) denote the family of all sum-free subsets of \(A\) of \({\mathcal A}\). It is proved in the paper that \[ 2^{\lfloor(p-2)/3\rfloor}(p-1)(1+O(2^{-\varepsilon p}))\leq |{\text{SF}}[\mathbb{Z}/p\mathbb{Z}]|\leq 2^{0.498 p} \] for sufficiently large primes \(p\) and with an absolute constant \(\varepsilon>0\). The authors note that they know no simple proof that \(|{\text{SF}}[\mathbb{Z}/p\mathbb{Z}]|\ll 2^{p/2}\). Concerning the lower bound, they prove more generally: Let \(I\) be a block of consecutive residue classes modulo a prime \(p\) such that \(|I