On sum-free sets modulo $p$

On sum-free sets modulo p

Let p be a sufficiently large prime and A be a sum-free subset of Z/pZ; improving on a previous result of V. F. Lev, we show that if |A| = card(A) > 0.324p, then A is contained in a dilation of the interval [|A| , p− |A|] (mod. p).

Conditions on Periodicity for Sum-Free Sets

Notes on sum-free and related sets

Our main topic is the number of subsets of 1; n] which are maximal with respect to some condition such as being sum-free, having no number dividing another, etc. We also investigate some related questions. In our earlier paper 8], we considered conditions on sets of positive integers (sum-freeness, Sidon sequences, etc.), and attempted to estimate the number of subsets of 1; n] satisfying each ...

Sum-Free Sets and Related Sets

A set A of integers is sum-free if A\(A+A) = ;. Cameron conjectured that the number of sum-free sets A f1; : : : ; Ng is O(2 N=2). As a step towards this conjecture, we prove that the number of sets A f1

Small Maximal Sum-Free Sets

Let G be a group and S a non-empty subset of G. If ab / ∈ S for any a, b ∈ S, then S is called sum-free. We show that if S is maximal by inclusion and no proper subset generates 〈S〉 then |S| ≤ 2. We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists a ∈ S such that a / ∈ 〈S \ {a}〉.