Nonexistence of certain regular maps of 2-power order

Abstract

In a recent paper, Hou et al. conjectured that there exist no regular maps of order \(2^n\) and of type \(\{2^k,2^s\}\), where n, k, and s are positive integers satisfying \(2\le s<k<n-1\) and \(s+k>n\). In this paper, we give an affirmative answer to this conjecture.