Sets with more differences than sums
Jan-Christoph Schlage-Puchta

TL;DR
This paper proves that for a random set of integers with density zero, the number of differences exceeds the number of sums almost always, confirming a conjecture by Martin and O'Bryant.
Contribution
It establishes that sparse random sets of integers typically have more differences than sums, confirming a longstanding conjecture.
Findings
Random sets with density zero have more differences than sums almost surely.
The conjecture by Martin and O'Bryant is proven.
The result applies to a broad class of sparse sets.
Abstract
We show that a random set of integers with density 0 has almost always more differences than sums. This proves a conjecture by Martin and O'Bryant.
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