Maximum number of sum-free colorings in finite abelian groups
نویسندگان
چکیده
منابع مشابه
Rainbow-free 3-colorings in abelian groups
A 3–coloring of an abelian group G is rainbow–free if there is no 3–term arithmetic progression with its members having pairwise distinct colors. We describe the structure of rainbow–free colorings of abelian groups. This structural description proves a conjecture of Jungić et al. on the size of the smallest chromatic class of a rainbow–free coloring of cyclic groups.
متن کاملSum-free subsets of finite abelian groups of type III
A finite abelian group G of order n is said to be of type III if all divisors of n are congruent to 1 modulo 3. We obtain a classification theorem for sum-free subsets of cardinality very “close” to the largest possible in a finite abelian group G of type III. This theorem, when taken together with known results, gives a complete characterisation of sum-free subsets of the largest cardinality i...
متن کاملRainbow-free 3-colorings of Abelian Groups
A 3–coloring of the elements of an abelian group is said to be rainbow–free if there is no 3–term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow–free colorings of abelian groups. This characterization proves a conjecture of Jungić et al. on the size of the smallest chromatic class of a rainbow–free 3–coloring of cyclic g...
متن کاملCounting Sum-free Sets in Abelian Groups
In this paper we study sum-free sets of order m in finite Abelian groups. We prove a general theorem about independent sets in 3-uniform hypergraphs, which allows us to deduce structural results in the sparse setting from stability results in the dense setting. As a consequence, we determine the typical structure and asymptotic number of sum-free sets of order m in Abelian groups G whose order ...
متن کاملSum-free Sets in Abelian Groups
Let A be a subset of an abelian group G with |G| = n. We say that A is sum-free if there do not exist x, y, z ∈ A with x+ y = z. We determine, for any G, the maximal density μ(G) of a sum-free subset of G. This was previously known only for certain G. We prove that the number of sum-free subsets of G is 2, which is tight up to the o-term. For certain groups, those with a small prime factor of t...
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: Israel Journal of Mathematics
سال: 2018
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-018-1705-1