Finding and Counting MSTD sets

Details Finding and Counting MSTD sets Finding and Counting MSTD sets

2011-07-14

arxiv.org/abs/1107.2719v1

Mathematics

Number Theory

This is a survey article based on talks given at CANT 2011 and work done at the SMALL 2011 program at Williams College

Scientific paper

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 constructions and results of generalized MSTD sets, including among other items results on a positive percentage of sets having a given linear combination greater than another linear combination, and a proof that a positive percentage of sets are $k$-generational sum-dominant (meaning $A$, $A+A$, $...$, $kA = A + ...+A$ are each sum-dominant).

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