The group of symmetries of the Tower of Hanoi graph
So Eun Park

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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Theories and Applications · Mathematics and Applications
