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 …

A Heffter array is an m by n matrix with nonzero entries from Z_ {2mn+ 1} such that i) every
row and column sum to 0, and ii) no element from {x,-x} appears twice. We construct some …

In 2015, Archdeacon introduced the notion of Heffter arrays and showed the connection
between Heffter arrays and biembedding m-cycle and an n-cycle systems on a surface. In …

Suppose and are arbitrary lists of positive integers. In this article, we determine necessary
and sufficient conditions on M and N for the existence of a simple graph G, which admits a …

An embedding of a digraph in an orientable surface is an embedding as the underlying
graph and arcs in each region force a directed cycle. The directed genus is the minimum …

In this paper we extend the study of Heffter arrays and the biembedding of graphs on
orientable surfaces first discussed by Archdeacon in 2014. We begin with the definitions of …

We describe a class of Skolem sequences of order n such that for the cyclic Steiner triple
system of order 6 n+ 1 generated by any Skolem sequence from the class we can construct …