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A conjecture on the Crazy Knight's Tour Problem
Lorenzo Mella, Anita Pasotti
Let be an toroidal array containing filled and empty cells. Fix an orientation of each row and an orientation of each column…
On relative simple Heffter spaces
Laura Johnson, Lorenzo Mella, Anita Pasotti
In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup of an…
Heffter arrays over partial loops
Raúl M. Falcón, Lorenzo Mella
A Heffter array over an additive group is any partially filled array satisfying that: (1) each one of its rows and columns sum to zero in , and (2) if $i\in G\setminus\{…
The Hadamard multiary quasigroup product
Raúl M. Falcón, L. Mella, P. VojtÄchovský
The Hadamard quasigroup product has recently been introduced as a natural generalization of the classical Hadamard product of matrices. It is defined as the superposition operator…
The extended irregular domination problem
Lorenzo Mella, Anita Pasotti
In this paper we introduce a new domination problem strongly related to the following one recently proposed by Broe, Chartrand and Zhang. One says that a vertex of a graph …
Constructing generalized Heffter arrays via near alternating sign matrices
Lorenzo Mella, Tommaso Traetta
Let be a subset of a group (not necessarily abelian) such that is empty or contains only elements of order , and let $\mathbf{h}=(h_1,\ldots, h_m)\in \mathb…