Shape of the asymptotic maximum sum-free sets in integer lattice grids
نویسندگان
چکیده
We determine the shape of all sum-free sets in {1,2,…,n}2 size close to maximum 35n2, solving a problem Elsholtz and Rackham. show that such asymptotic lie completely stripe 45n−o(n)≤x+y≤85n+o(n). also for any positive integer p subset A⊆{1,2,…,n}2 which forbids triple (x,y,z) satisfying px+py=z.
منابع مشابه
Asymptotic formula for sum-free sets in abelian groups
Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x+ y = z, with x, y, z belonging to the set A. Let SF (G) the sel of all sum-free subets of G and σ(G) deonotes the number n(log 2 |SF (G)|). In this article we shall improve the error term in asymptotic formula of σ(G) obtained in [GR05]. The methods used are a slight refinement of ...
متن کاملLattice-free sets, branching disjunctions, and mixed-integer programming
In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and structured disjunctive cuts, especially the t-branch split cuts introduced by Li and Richard (2008). By analyzing n-dimensional lattice-free sets, we prove that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set wit...
متن کاملTHE INTERNAL IDEAL LATTICE IN THE TOPOS OF M-SETS
We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the categ...
متن کاملdetermination of maximal singularity free zones in the workspace of parallel manipulator
due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...
15 صفحه اولInteger Sum Sets Containing Long Arithmetic Progressions
the Schnirelmann and lower asymptotic densities respectively of d. According to Schnirelmann theory (see [9]), if 1 > as/ > 0 and Oes/ then a(2s/) ^ 2a(s/)-a(s/) > a(s/); and if a(s/)^\ then 2s/ = No. From this it follows that if as/ > 0 then there exists a positive integer k such that s/ is a basis of order k (that is, ks/ = No). According to Kneser's theorem [6], if dsf > 0 and Oes/ then eith...
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: European Journal of Combinatorics
سال: 2023
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2022.103614