Finding and Counting MSTD sets
Abstract
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 sumdominant (meaning $A$, $A+A$, $...$, $kA = A + ...+A$ are each sumdominant).
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 arXiv:
 arXiv:1107.2719
 Bibcode:
 2011arXiv1107.2719I
 Keywords:

 Mathematics  Number Theory;
 11P99
 EPrint:
 This is a survey article based on talks given at CANT 2011 and work done at the SMALL 2011 program at Williams College