Non-averaging sets
Algebraic and Analytic Methods in Combinatorics March 17, 2025 - March 21, 2025
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Non-averaging sets
A set of integers A is non-averaging if no element of A is an average of two or more other elements of A. We show that the largest non-averaging subset in [n] has size n^{1/4+o(1)}, resolving a problem of Erdos and Straus. Our proof combines convex geometric arguments with a structure theorem for subset sums. Joint work with Huy Pham.
Non-averaging sets
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