Heffter arrays were introduced by Archdeacon in 2015 as an interesting link between
combinatorial designs and topological graph theory. Since the initial paper on this topic …

Let S be a subset of a group G (not necessarily abelian) such that S∩− S is empty or
contains only elements of order 2, and let h=(h 1,…, hm)∈ N m and k=(k 1,…, kn)∈ N n. A …

In this paper we introduce a new class of partially filled arrays that, as Heffter arrays, are
related to difference families, graph decompositions and biembeddings. A non-zero sum …

Relative Heffter arrays, denoted by $\mathrm {H} _t (m, n; s, k) $, have been introduced as a
generalization of the classical concept of Heffter array. A $\mathrm {H} _t (m, n; s, k) $ is an …

In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐
colorable embeddings of cycle decompositions of the complete graph. Specifically, for n≡ 1 …

Square Heffter arrays are n× n arrays such that each row and each column contains k filled
cells, each row and column sum is divisible by 2 n k+ 1 and either x or− x appears in the …

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

An ${\ell} $-cycle system ${\mathcal F} $ of a graph $\Gamma $ is a set of ${\ell} $-cycles
which partition the edge set of $\Gamma $. Two such cycle systems ${\mathcal F} $ and …

In this paper we study a tour problem that we came cross while studying biembeddings and
Heffter arrays, see [DS Archdeacon, Heffter arrays and biembedding graphs on surfaces …

In this paper, we consider the following conjecture, proposed by Brian Alspach, concerning
partial sums in finite cyclic groups: given a subset A of Z _n ∖ {0\} Z n {0 of size k such that ∑ …