Simone Costa

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20222026

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math.CO2026

An Improved Upper Bound for Recovering Pairs

Simone Costa

We prove that every recovering pair $(A, B)$ of nonempty families of subsets of an $n$ -element set satisfies $$|\mathcal{A}||\mathcal{B}|\le\left(\frac{223949}{1…

math.CO2026

A negative answer to the Erdős-Sárkőzy question

Simone Costa

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 $A \subseteq {1, \dots, N}$ has $H(…

math.CO2026

A bandwidth refinement of the Erdős distinct subset sums bound

Simone Costa, Stefano Della Fiore

Let $f (n)$ be the least possible largest element of an $n$ -element set of positive integers with pairwise distinct subset sums. Dubroff, Fox and Xu proved the finite lower bound \[…

math.CO2026

Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

Simone Costa, Stefano Della Fiore, Mattia Fontana

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 d…

math.PR2026

Anticoncentration of Random Sums in $Z_{p}$

Simone Costa

In this paper we investigate the probability distribution of the sum $Y$ of $ℓ$ independent identically distributed random variables taking values in $Z_{p}$ . Our main fo…

An Improved Upper Bound for Recovering Pairs

A negative answer to the Erdős-Sárkőzy question

A bandwidth refinement of the Erdős distinct subset sums bound

Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

Anticoncentration of Random Sums in Zp​

Anticoncentration of Random Sums in $Z_{p}$