Fringe Pairs in Generalized MSTD Sets

Abstract

A More Sums Than Differences (MSTD) set is a set A for which |A+A|j > jA - 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. We extend this notion and study decompositions of intervals {0, 1,…, n} into MSTD sets and prove that a positive proportion of decompositions into two sets have the property that both sets are MSTD.