KuloğLu, Bahar; Özkan, Engin; Shannon, Anthony G.

In this paper, the Narayana sequence modulo m is studied. The paper outlines the definition of Narayana numbers and some of their combinatorial links with Eulerian, Catalan and Delannoy numbers and other special functions. From the definition, the Narayana orbit of a 2-generator group for a generating pair (x, y) ∈ G is defined, so that the lengths of the period of the Narayana orbit can be examined. These yield in turn the Narayana lengths of the polyhedral group and the binary polyhedral group for the generating pair (x, y) and associated properties.