Sum-free sets in abelian groups
| dc.creator | Green, Ben | |
| dc.creator | Ruzsa, Imre Z. | |
| dc.date | 2003-07-10 | |
| dc.date | 2004-11-18 | |
| dc.date.accessioned | 2026-07-07T04:59:34Z | |
| dc.date.available | 2026-07-07T04:59:34Z | |
| dc.description | Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z in A satisfying x + y = z. We determine, for any G, the cardinality of the largest sum-free subset of G. This equals c(G)|G| where c(G) is a constant depending on G and lying in the interval [2/7,1/2]. We also estimate the number of sum-free subsets of G. It turns out that log_2 of this number is c(G)|G| + o(|G|), which is tight up to the o-term. For certain abelian groups, those whose order is divisible by a small prime of the form 3k + 2, we can obtain an asymptotic for the number of sum-free sets. | |
| dc.description | 25 pages, even more revisions and corrections | |
| dc.identifier | https://arxiv.org/abs/math/0307142 | |
| dc.identifier | http://arxiv.org/abs/math/0307142 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68040 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11B75; 20D60; 20K01 | |
| dc.title | Sum-free sets in abelian groups | |
| dc.type | text |