Simple Explicit Formulas for the Frame-Stewart Numbers

  title={Simple Explicit Formulas for the Frame-Stewart Numbers},
  author={Sandi Klav{\vz}ar and Uro{\vs} Milutinovi{\'c}},
  journal={Annals of Combinatorics},
Abstract. Several different approaches to the multi-peg Tower of Hanoi problem are equivalent. One of them is Stewart's recursive formula ¶¶$ S (n, p) = min \{2S (n_1, p) + S (n-n_1, p-1)\mid n_1, n-n_1 \in \mathbb{Z}^+\}. $¶¶In the present paper we significantly simplify the explicit calculation of the Frame-Stewart's numbers S(n, p) and give a short proof of the domain theorem that describes the set of all pairs (n, n1), such that the above minima are achieved at n1. 

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