##
**
When Sets Can and Cannot Have Sum-Dominant Subsets
**

###
Hùng Việt Chu

Department of Mathematics

Washington and Lee University

Lexington, VA 24450

USA

Nathan McNew

Department of Mathematics

Towson University

Towson, MD 21252

USA

Steven J. Miller

Department of Mathematics

Williams College

Williamstown, MA 01267

USA

Victor Xu and Sean Zhang

Department of Mathematics

Carnegie Mellon University

Pittsburgh, PA 15213

USA

**Abstract:**

A finite set of integers A is a sum-dominant (also called a More
Sums Than Differences or MSTD) set if |A+A| > |A−A|. While almost
all subsets of {0,...,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.

**
Full version: pdf,
dvi,
ps,
latex
**

Received June 1 2018; revised versions received August 21 2018; November
13 2018; November 16 2018. Published in *Journal of Integer
Sequences*, November 23 2018.

Return to
**Journal of Integer Sequences home page**