Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
نویسندگان
چکیده
منابع مشابه
Some explicit constructions of sets with more sums than differences
We present a variety of new results on finite sets A of integers for which the sumset A + A is larger than the difference set A − A, socalled MSTD (more sums than differences) sets. First we show that there is, up to affine transformation, a unique MSTD subset of Z of size 8. Secondly, starting from some examples of size 9, we present several new constructions of infinite families of MSTD sets....
متن کاملSets with More Sums than Differences
Let A be a finite subset of the integers or, more generally, of any abelian group, written additively. The set A has more sums than differences if |A + A| > |A − A|. A set with this property is called an MSTD set. This paper gives explicit constructions of families of MSTD sets of integers.
متن کاملD ec 2 01 1 GENERALIZED MORE SUMS THAN DIFFERENCES SETS
A More Sums Than Differences (MSTD, or sum-dominant) set is a finite set A ⊂ Z such that |A+A| < |A−A|. Though it was believed that the percentage of subsets of {0, . . . , n} that are sum-dominant tends to zero, in 2006 Martin and O’Bryant [MO] proved that a positive percentage are sum-dominant. We generalize their result to the many different ways of taking sums and differences of a set. We p...
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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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We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k = s1 + s2, si ∈ S; such sets are called Sidon sets if g = 2 and generalized Sidon sets (or B2[ ⌈ g/2 ⌉ ] sets) if g ≥ 3. We extend to generalized Sidon sets the Sidon-set constructions of Singer, Bose, and Ruzsa. We also further optimize Koulantzakis’ idea of interleaving sever...
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ژورنال
عنوان ژورنال: Integers
سال: 2012
ISSN: 1867-0652,1867-0652
DOI: 10.1515/integers-2012-0015