Random sum-free subsets of abelian groups

Details Random sum-free subsets of abelian groups Random sum-free subsets of abelian groups

2011-03-10

arxiv.org/abs/1103.2041v1

Mathematics

Combinatorics

30 pages

Scientific paper

We characterize the structure of maximum-size sum-free subsets of a random subset of an abelian group $G$. In particular, we determine the threshold $p_c \approx \sqrt{\log n / n}$ above which, with high probability as $|G| \to \infty$, each such subset is contained in a maximum-size sum-free subset of $G$, whenever $q$ divides $|G|$ for some (fixed) prime $q$ with $q \equiv 2 \pmod 3$. Moreover, in the special case $G = \ZZ_{2n}$, we determine a sharp threshold for the above property. The proof uses recent 'transference' theorems of Conlon and Gowers, together with stability theorems for sum-free sets of abelian groups.

Affiliated with

Also associated with

No associations

Rating

Random sum-free subsets of abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random sum-free subsets of abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random sum-free subsets of abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-631457