Combinatorics of Topmost Discs of Multi-Peg Tower of Hanoi Problem

Abstract

Combinatorial properties of the multi-peg Tower of Hanoi problem on $n$ discs and $p$ pegs are studied. Top-maps are introduced as maps which reflect topmost discs of regular states. We study these maps from several points of view. We also count the number of edges
in graphs of the multi-peg Tower of Hanoi problem and in this way obtain some combinatorial identities.