F. Morini

activity

20172022

collaborators

6 papers

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

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

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…

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

A problem on partial sums in abelian groups

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