Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Constructions of Large Families of Generalized More Sums Than
  Differences Sets   A More Sums Than Differences (MSTD) set is a set of integers A contained in
{0, ..., n-1} whose sumset A+A is larger than its difference set A-A. While it
is known that as n tends to infinity a positive percentage of subsets of {0,
..., n-1} are MSTD sets, the methods to prove this are probabilistic and do not
yield nice, explicit constructions. Recently Miller, Orosz and Scheinerman gave
explicit constructions of a large family of MSTD sets; though their density is
less than a positive percentage, their family's density among subsets of {0,
..., n-1} is at least C/n^4 for some C>0, significantly larger than the
previous constructions, which were on the order of 1 / 2^{n/2}. We generalize
their method and explicitly construct a large family of sets A with |A+A+A+A| >
|(A+A)-(A+A)|. The additional sums and differences allow us greater freedom
than in Miller, Orosz and Scheinerman, and we find that for any epsilon>0 the
density of such sets is at least C / n^epsilon. In the course of constructing
such sets we find that for any integer k there is an A such that |A+A+A+A| -
|A+A-A-A| = k, and show that the minimum span of such a set is 30.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga