Small Maximal Sum-Free Sets
نویسندگان
چکیده
منابع مشابه
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}〉.
متن کاملZero-sum free sets with small sum-set
Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.
متن کاملBounds on the Number of Maximal Sum-Free Sets
We show that the number of maximal sum-free subsets of {1, 2, . . . , n} is at most 2. We also show that 2 is an upper bound on the number of maximal product-free subsets of any group of order n.
متن کاملOn the maximal density of sum-free sets
Theorem 1 is due to Folkman [4], who also asked whether its assertion remains true if ε > 0 is replaced by a function which tends to 0 as n→∞. Theorem 2 below states that this is indeed the case and, furthermore, for every set A dense enough, one can take b = 0. It should be mentioned that recently a similar result has been independently proved by Hegyvári [5], who showed that the assertion of ...
متن کاملOn the Number of Maximal Sum-free Sets
It is shown that the set {1, 2, . . . , n} contains at most 2n/2−2n maximal sum-free subsets, provided n is large enough. A set A ⊆ [n] = {1, 2, . . . , n} is sum-free if for any two elements a, b ∈ A we have a + b / ∈ A. A sum-free set A ⊆ [n] is maximal if it is not contained in any other sum-free subset of [n]. Let s(n) and smax(n) denote the number of sum-free and maximal sum-free subsets o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/148