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arXiv · 1608.03256

When Sets Can and Cannot Have MSTD Subsets

Hung Chu·Nathan McNew·Steven J. Miller·Victor Xu·Sean Zhang
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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.

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Hung Chu, Nathan McNew, Steven J. Miller, Victor Xu, Sean Zhang. 2016-08-10. When Sets Can and Cannot Have MSTD Subsets. https://arxiv.org/abs/1608.03256

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