Simone Costa

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20222026

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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…

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

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