Coincidences in numbers of graph vertices corresponding to regular planar hyperbolic mosaics

Abstract

The aim of this paper is to determine the elements which are in two pairs of sequences linked to the regular mosaics $\{4,5\}$ and $\{p,q\}$ on the hyperbolic plane. The problem leads to the solution of diophantine equations of certain types.Comment: 10 pages, 2 figures, Annales Mathematicae et Informaticae 43 (2014