Marco Antonio Pellegrini

collaborators

4 papers

math.CO2025

An update on the existence of integer Heffter arrays

Fiorenza Morini, Marco Antonio Pellegrini

An integer Heffter array $H (m, n; s; k)$ is an $m \times n$ partially filled array whose entries are the elements of a subset $Ω \subset Z$ such that ${Ω, - Ω}$ is a partition…

math.CO2024

Signed magic arrays: existence and constructions

Fiorenza Morini, Marco Antonio Pellegrini

Let $m, n, s, k$ be four integers such that $1 ⩽ s ⩽ n$ , $1 ⩽ k ⩽ m$ and $m s = nk$ . A signed magic array $S M A (m, n; s, k)$ is an $m \times n$ partially filled…

math.CO2024

On a conjecture by Sylwia Cichacz and Tomasz Hinc, and a related problem

Fiorenza Morini, Marco Antonio Pellegrini, Stefania Sora

A $Γ$ -magic rectangle set $MRS_{Γ} (a, b; c)$ is a collection of $c$ arrays of size $a \times b$ whose entries are the elements of an abelian group $Γ$ of order $ab c$ , each on…

math.CO2024

Towards a solution of Archdeacon's conjecture on integer Heffter arrays

Marco Antonio Pellegrini, Tommaso Traetta

In this paper, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays $H (m, n; s, k)$ whenever the necessary conditions hol…