Author

Simone Costa

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Preprint Sep 2026

A negative answer to the Erd\H{o}s-S\'ark\H{o}zy question

For a finite set $A$ of positive integers, let $H(A)$ be its set of subset sums, and let $g_3(n)$ be the least $N$ for which some $n$-element set $A\subseteq\{1,\ldots,N\}$ has $H(A)$ free of nonconstant three-term arithmetic progressions. Erd\H{o}s and S\'ark\H{o}zy asked whether $g_3(n)\gg 3^n$. We prove \[ \liminf_{...

Simone Costa · 0 citations

Preprint Jul 2026

Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

We study polynomial zero-avoidance over finite vector spaces by means of slice rank and partition rank. We first make the support-entropy method effective by showing how a finite dual certificate yields an explicit entropy gap whenever the coefficient support admits no probability distribution with uniform marginals. F...

Simone Costa, Stefano Della Fiore, Mattia Fontana · 0 citations