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

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10 papers · 1 filter

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…

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

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