Some Results Associated with the Diagonals of Derived Plane Permutations

Abstract

A plane permutation is a pair p = (s, π) where s is an n-cycle and π is an arbitrary permutation. In this paper, we study the properties of p under two instances; when π = s and π = s −1 . We also define the diagonal of the derived plane permutation and establish that it coincides with the diagonal of the underlying plane permutation.