4 citations · 5 across the 10 of their papers we have counts for
11 papers
Completing the Existence Problem for Integer Relative Heffter Arrays
Lorenzo Mella
Heffter arrays, introduced by Archdeacon in 2015, are combinatorial structures with applications to cyclic cycle systems and biembeddings of graphs on surfaces. Costa, Morini, Paso…
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. Vojtěchovský
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 …
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…
A solution to the 7-prince's tour problem
Lorenzo Mella
In [1] the authors studied the closed tour problem on the chessboard of a chess piece, called -prince, leaving open the existence of such a tour when . In this…
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…
Weak Heffter Arrays and biembedding graphs on non-orientable surfaces
Simone Costa, Lorenzo Mella, Anita Pasotti
In 2015, Archdeacon proposed the notion of Heffter arrays in view of its connection to several other combinatorial objects. In the same paper he also presented the following varian…
A class of highly symmetric Archdeacon embeddings
Simone Costa, Lorenzo Mella
Archdeacon, in his seminal paper , defined the concept of Heffter array to provide explicit constructions of biembeddings of the complete graph into orientable surfaces,…
Tight globally simple non-zero sum Heffter arrays and biembeddings
Lorenzo Mella, Anita Pasotti
Square relative non-zero sum Heffter arrays, denoted by , have been introduced as a variant of the classical concept of Heffter array. An $\mathrm{N}\m…