A Survey of Heffter Arrays

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, there has been a good deal of interest in Heffter arrays. This survey presents an overview of the current state of the art of this topic. We begin with an introduction to Heffter arrays for the reader who is unfamiliar with the subject. Then we give a unified and comprehensive presentation of the major results, showing some proof methods. Connections of Heffter arrays to several other combinatorial objects are discussed, such as problems on partial sums and sequenceability, biembedding graphs on surfaces, difference families, and orthogonal graph decompositions. Then, proposed variants and generalizations of Heffter arrays are examined. A list of unsolved problems and an updated and complete bibliography are provided.