Sets with Few Differences in Abelian Groups
نویسندگان
چکیده
منابع مشابه
Difference sets in abelian 2-groups
If G is an abelian group of order u, and D is a subset of G with k elements such that every nonidentity element can be expressed 2 times in the form a b, where a and b are elements of D, then D is called a (u, k, A) difference set in G. The order n of the difference set is k 1. In this paper we consider the parameter values v = 22di 2, k = 22d+ ’ 24 ,I= 22d 2d, and n=22d. The rank r of G is the...
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 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 کاملCounting MSTD Sets in Finite Abelian Groups
In an abelian group G, a more sums than differences (MSTD) set is a subset A ⊂ G such that |A+A| > |A−A|. We provide asymptotics for the number of MSTD sets in finite abelian groups, extending previous results of Nathanson. The proof contains an application of a recently resolved conjecture of Alon and Kahn on the number of independent sets in a regular graph.
متن کاملProper Moufang Sets with Abelian Root Groups Are Special
Moufang sets are the Moufang buildings of rank one. They were introduced by J. Tits [T1] as a tool for studying algebraic groups of relative rank one. They are essentially equivalent to split BN -pairs of rank one, and as such they have been studied extensively. In some sense they are the basic ‘building blocks’ of all split BN -pairs. In the finite case, it had been a major project to classify...
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: 2018
ISSN: 1077-8926
DOI: 10.37236/5502