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                * Princeton Discrete Math Seminar *
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Speaker: Noah Kravitz (U Oxford)

Thursday 24th September, 3:00 in Fine Hall 224.

Title: The structure of sets with few subset sums

An old result of Nathanson shows that every n-element 
set of positive reals has at least n(n+1)/2+1 distinct subset sums, 
with equality exactly for homogeneous arithmetic progressions. 
We establish stability versions of this inverse theorem in two 
regimes. First, for any parameter M at most n-4, we
precisely characterize the n-element sets of positive reals with 
at most n(n+1)/2+1+M subset sums. Second, for any constant C, 
we provide a characterization, sharp up to constants, of the 
n-element sets of positive reals with at most Cn^2 subset sums.

Joint work with Ruben Carpenter and Colin Defant.

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