F. Morini

activity

20102025

most citedGlobally simple Heffter arrays and orthogonal cyclic cycle decompositions

23 citations · 25 across the 7 of their papers we have counts for

collaborators

11 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.CO2022

Magic partially filled arrays on abelian groups

Fiorenza Morini, Marco Antonio Pellegrini

In this paper we introduce a special class of partially filled arrays. A magic partially filled array $MPF_{Ω} (m, n; s, k)$ on a subset $Ω$ of an abelian group $(Γ, +)$ is a pa…

math.CO2021

Rectangular Heffter arrays: a reduction theorem

Fiorenza Morini, Marco Antonio Pellegrini

Let $m, n, s, k$ be four integers such that $3 \leq s \leq n$ , $3 \leq k \leq m$ and $m s = nk$ . Set $d = g cd (s, k)$ . In this paper we show how one can construct a Heffter array $H (m, n; s, k)$ …

math.CO2020★ 1 cited

Magic rectangles, signed magic arrays and integer $λ$ -fold relative Heffter arrays

Fiorenza Morini, Marco Antonio Pellegrini

Let $m, n, s, k$ be integers such that $4 \leq s \leq n$ , $4 \leq k \leq m$ and $m s = nk$ . Let $λ$ be a divisor of $2 m s$ and let $t$ be a divisor of $\frac{2 m s}{λ}$ . In this paper we constru…

math.CO2019

On the existence of integer relative Heffter arrays

Fiorenza Morini, Marco Antonio Pellegrini

Let $v = 2 m s + t$ be a positive integer, where $t$ divides $2 m s$ , and let $J$ be the subgroup of order $t$ of the cyclic group $Z_{v}$ . An integer Heffter array $H_{t} (m, n; s, k)$ o…

math.CO2019

A generalization of Heffter arrays

Simone Costa, Fiorenza Morini, Anita Pasotti +1

In this paper we define a new class of partially filled arrays, called relative Heffter arrays, that are a generalization of the Heffter arrays introduced by Archdeacon in 2015. Le…

math.CO2017★ 23 cited

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

Simone Costa, Fiorenza Morini, Anita Pasotti +1

In this paper we introduce a particular class of Heffter arrays, called globally simple Heffter arrays, whose existence gives at once orthogonal cyclic cycle decompositions of the…

math.CO2017

A problem on partial sums in abelian groups

Simone Costa, Fiorenza Morini, Anita Pasotti +1

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, w…

math.RA2010★ 1 cited

Circular planar nearrings: geometrical and combinatorial aspects

Anna Benini, Achille Frigeri, Fiorenza Morini

Let $(N, Φ)$ be a circular Ferrero pair. We define the disk with center $b$ and radius $a$ , $D (a; b)$ , as \[\mathcal{D}(a;b)=\{x\in Φ(r)+c\mid r\neq 0,\ b\in Φ(r)+c,\ |(Φ(r…

An update on the existence of integer Heffter arrays

Signed magic arrays: existence and constructions

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

Magic partially filled arrays on abelian groups

Rectangular Heffter arrays: a reduction theorem

Magic rectangles, signed magic arrays and integer λ-fold relative Heffter arrays

On the existence of integer relative Heffter arrays

A generalization of Heffter arrays

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

A problem on partial sums in abelian groups

Circular planar nearrings: geometrical and combinatorial aspects

Magic rectangles, signed magic arrays and integer $λ$ -fold relative Heffter arrays