A class of highly symmetric Archdeacon embeddings

Archdeacon, in his seminal paper in Electron. J. Combin. (2015), defined the concept of Heffter array to provide explicit constructions of biembeddings of the complete graph Kv into orientable surfaces, the so-called Archdeacon embeddings, and proved that these embeddings are Zv-regular. In this paper, we show that an Archdeacon embedding may admit an automorphism group that is strictly larger than Zv . Indeed, as an application of the interesting class of arrays recently introduced by Buratti in https://arxiv.org/abs/2210.16672, we exhibit, for infinitely many values of v, an embedding of this type having full automorphism group of size (Formula Presented) that is the largest possible one.