Simone Costa

activity

20222026

collaborators

11 papers

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…

math.CO2025

Graham's rearrangement for a class of semidirect products

Simone Costa, Stefano Della Fiore, Eva R. Engel

A famous conjecture of Graham asserts that every set $A \subseteq Z_{p} ∖ {0}$ can be ordered so that all partial sums are distinct. Bedert and Kravitz proved that…

math.CO2024

Orthogonal and oriented Fano planes, triangular embeddings of $K_{7},$ and geometrical representations of the Frobenius group $F_{21}$

Simone Costa, Marco Pavone

In this paper we present some geometrical representations of the Frobenius group of order $21$ (henceforth, $F_{21}$ ). The main focus is on investigating the group of common automo…

math.CO2024

Weak Freiman isomorphisms and sequencings of small sets

Simone Costa, Stefano Della Fiore

In this paper, we introduce a weakening of the Freiman isomorphisms between subsets of non necessarily abelian groups. Inspired by the breakthrough result of Kravitz, [14], on cycl…

math.CO2024

Weak multiset sequenceability and weak BHR conjecture

Simone Costa

A subset $S$ of a group $(G, +)$ is $t$ -weakly sequenceable if there is an ordering $(y_{1}, \dots, y_{k})$ of its elements such that the partial sums~ $s_{0}, s_{1}, \dots, s_{k}$ , given by…

math.CO2024

Variants of the Erdős distinct sums problem and variance method

Simone Costa, Stefano Della Fiore, Andrea Ferraguti

Let $Σ = {a_{1}, \dots, a_{n}}$ be a set of positive integers with $a_{1} < \dots < a_{n}$ such that all $2^{n}$ subset sums are pairwise distinct. A famous conjecture of Erdős states tha…

math.CO2022

Bounds on the Higher Degree Erdős-Ginzburg-Ziv Constants over $F_{q}^{n}$

Simone Costa, Stefano Della Fiore

The classical Erdős-Ginzburg-Ziv constant of a group $G$ denotes the smallest positive integer $ℓ$ such that any sequence $S$ of length at least $ℓ$ contains a zero-sum subse…

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​

Graham's rearrangement for a class of semidirect products

Orthogonal and oriented Fano planes, triangular embeddings of K7​, and geometrical representations of the Frobenius group F21​

Weak Freiman isomorphisms and sequencings of small sets

Weak multiset sequenceability and weak BHR conjecture

Variants of the Erdős distinct sums problem and variance method

Bounds on the Higher Degree Erdős-Ginzburg-Ziv Constants over Fqn​

Anticoncentration of Random Sums in $Z_{p}$

Orthogonal and oriented Fano planes, triangular embeddings of $K_{7},$ and geometrical representations of the Frobenius group $F_{21}$

Bounds on the Higher Degree Erdős-Ginzburg-Ziv Constants over $F_{q}^{n}$