منابع مشابه
Fringe Pairs in Generalized Mstd Sets
A More Sums Than Differences (MSTD) set is a set A for which |A+A| > |A−A|. Martin and O’Bryant proved that the proportion of MSTD sets in {0, 1, . . . , n} is bounded below by a positive number as n goes to infinity. Iyer, Lazarev, Miller and Zhang introduced the notion of a generalized MSTD set, a set A for which |sA− dA| > |σA − δA| for a prescribed s + d = σ + δ. We offer efficient construc...
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 کاملFinding and Counting MSTD sets
We review the basic theory of More Sums Than Differences (MSTD) sets, specifically their existence, simple constructions of infinite families, the proof that a positive percentage of sets under the uniform binomial model are MSTD but not if the probability that each element is chosen tends to zero, and ‘explicit’ constructions of large families of MSTD sets. We conclude with some new constructi...
متن کاملConstructing MSTD Sets Using Bidirectional Ballot Sequences
A more sums than differences (MSTD) set is a finite subset S of the integers such that |S + S| > |S − S|. We construct a new dense family of MSTD subsets of {0, 1, 2, . . . , n − 1}. Our construction gives Θ(2n/n) MSTD sets, improving the previous best construction with Ω(2/n) MSTD sets by Miller, Orosz, and Scheinerman.
متن کاملExplicit Constructions of Infinite Families of Mstd Sets
We explicitly construct infinite families of MSTD (more sums than differences) sets, i.e., sets where |A+A| > |A−A|. There are enough of these sets to prove that there exists a constant C such that at least C/r of the 2 subsets of {1, . . . , r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2 for some polynomial f(r)). We co...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042117501470