The group of symmetries of the Tower of Hanoi graph

TL;DR

This paper proves that the symmetry group of the Tower of Hanoi graph with k pegs and n disks is isomorphic to the permutation group of k elements, S_k, for all k ≥ 3 and positive n.

Contribution

It establishes a complete characterization of the symmetry group of the Tower of Hanoi graph as isomorphic to S_k for all relevant parameters.

Findings

The symmetry group is isomorphic to S_k.

This holds for all k ≥ 3 and n ≥ 1.

Provides a group-theoretic understanding of the Hanoi graph symmetries.

Abstract

I prove that the group of symmetries of the Tower of Hanoi graph with k pegs and n disks, denoted H_n^k, is isomorphic to the group of permutations of k elements, S_k, for all k greater than or equal to 3 and positive n.