When Sets Can and Cannot Have MSTD Subsets

Abstract

A finite set of integers $A$ is a sum-dominant (also called an More Sums Than Differences or MSTD) set if $|A+A|>|A-A|$. While almost all subsets of $\{0,\dots ,n\}$ are not sum-dominant, interestingly a small positive percentage are. We explore sufficient conditions on infinite sets of positive integers such that there are either no sum-dominant subsets, at most finitely many sum-dominant subsets, or infinitely many sum-dominant subsets. In particular, we prove no subset of the Fibonacci numbers is a sum-dominant set, establish conditions such that solutions to a recurrence relation have only finitely many sum-dominant subsets, and show there are infinitely many sum-dominant subsets of the primes.

Version 2.2, 13 pages. Strengthened Theorem 1.1, fixed some typos, clarified exposition

References in corpus (1)

• Constructing MSTD Sets Using Bidirectional Ballot Sequences

Cited by in corpus (2)

• Distribution of missing differences in diffsets
• Generalizing the Distribution of Missing Sums in Sumsets