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The Explicit Formula of the Presumed Optimal Recurrence Relation for the Star Tower of Hanoi
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In this paper, we show the explicit formula of the recurrence relation for the Tower of Hanoi on the star graph with four vertices, where the perfect tower of disks on a leaf vertex is transferred to the central vertex. This gives the solution to the problem posed at the 17th International Conference on Fibonacci Numbers and Their Applications[11]. Then, the recurrence relation are generalized to include the ones for the original 4-peg Tower of Hanoi and the Star Tower of Hanoi of transferring the tower from a leaf to another.
- Publication
- IEICE TRANSACTIONS on Information Vol.E102-D No.3 pp.492-498
- Publication Date
- 2019/03/01
- Publicized
- 2018/10/30
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2018FCP0013
- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science — Algorithm, Theory of Computation, and their Applications —)
- Category
Authors
Akihiro MATSUURA
Tokyo Denki University
Yoshiaki SHOJI
Tokyo Denki University
Keyword
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Akihiro MATSUURA, Yoshiaki SHOJI, "The Explicit Formula of the Presumed Optimal Recurrence Relation for the Star Tower of Hanoi" in IEICE TRANSACTIONS on Information,
vol. E102-D, no. 3, pp. 492-498, March 2019, doi: 10.1587/transinf.2018FCP0013.
Abstract: In this paper, we show the explicit formula of the recurrence relation for the Tower of Hanoi on the star graph with four vertices, where the perfect tower of disks on a leaf vertex is transferred to the central vertex. This gives the solution to the problem posed at the 17th International Conference on Fibonacci Numbers and Their Applications[11]. Then, the recurrence relation are generalized to include the ones for the original 4-peg Tower of Hanoi and the Star Tower of Hanoi of transferring the tower from a leaf to another.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2018FCP0013/_p
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@ARTICLE{e102-d_3_492,
author={Akihiro MATSUURA, Yoshiaki SHOJI, },
journal={IEICE TRANSACTIONS on Information},
title={The Explicit Formula of the Presumed Optimal Recurrence Relation for the Star Tower of Hanoi},
year={2019},
volume={E102-D},
number={3},
pages={492-498},
abstract={In this paper, we show the explicit formula of the recurrence relation for the Tower of Hanoi on the star graph with four vertices, where the perfect tower of disks on a leaf vertex is transferred to the central vertex. This gives the solution to the problem posed at the 17th International Conference on Fibonacci Numbers and Their Applications[11]. Then, the recurrence relation are generalized to include the ones for the original 4-peg Tower of Hanoi and the Star Tower of Hanoi of transferring the tower from a leaf to another.},
keywords={},
doi={10.1587/transinf.2018FCP0013},
ISSN={1745-1361},
month={March},}
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TY - JOUR
TI - The Explicit Formula of the Presumed Optimal Recurrence Relation for the Star Tower of Hanoi
T2 - IEICE TRANSACTIONS on Information
SP - 492
EP - 498
AU - Akihiro MATSUURA
AU - Yoshiaki SHOJI
PY - 2019
DO - 10.1587/transinf.2018FCP0013
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E102-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2019
AB - In this paper, we show the explicit formula of the recurrence relation for the Tower of Hanoi on the star graph with four vertices, where the perfect tower of disks on a leaf vertex is transferred to the central vertex. This gives the solution to the problem posed at the 17th International Conference on Fibonacci Numbers and Their Applications[11]. Then, the recurrence relation are generalized to include the ones for the original 4-peg Tower of Hanoi and the Star Tower of Hanoi of transferring the tower from a leaf to another.
ER -
English
