Variants of (s,t)-Wythoff’s game

In this paper, we study four games, they are all restrictions of (s,t)-Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of (s,t)-Wythoff’s game, where a player is restricted to remove a multiple of K tokens in each move (K is a fixed positive integer)...

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Published inDiscrete Applied Mathematics Vol. 227; pp. 1 - 12
Main Authors Li, Haiyan, Liu, Sanyang, Fraenkel, Aviezri S., Liu, Wen An
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 20.08.2017
Elsevier BV
Subjects
[formula omitted]-position
[formula omitted]-Wythoff’s game
Applied mathematics
Combinatorics
Constrictions
Games
Normal play convention
Restriction
Restriction
Normal play convention
P-position
(s,t)-Wythoff’s game
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Abstract In this paper, we study four games, they are all restrictions of (s,t)-Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of (s,t)-Wythoff’s game, where a player is restricted to remove a multiple of K tokens in each move (K is a fixed positive integer). The others we called rook type restrictions of (s,t)-Wythoff’s game, including Odd-Arbitrary-Nim (s,t)-Wythoff’s Game, Odd–Odd-Nim (s,t)-Wythoff’s Game and Odd–Even-Nim (s,t)-Wythoff’s Game. In these three games, the restrictions are only made on horizontal and vertical moves, but not on the extended diagonal moves. For any K,s,t≥1, the sets of P-positions of our games are given in both normal and misère play.
AbstractList In this paper, we study four games, they are all restrictions of (s, t)-Wythoff's game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of (s, t)-Wythoff's game, where a player is restricted to remove a multiple of image tokens in each move (K is a fixed positive integer). The others we called rook type restrictions of (s, t)-Wythoff's game, including Odd-Arbitrary-Nim (s, t)-Wythoff's Game, Odd-Odd-Nim (s, t)-Wythoff's Game and Odd-Even-Nim (s, t)-Wythoff's Game. In these three games, the restrictions are only made on horizontal and vertical moves, but not on the extended diagonal moves. For any K, s, t ≥, the sets of P-positions of our games are given in both normal and misère play.
In this paper, we study four games, they are all restrictions of (s,t)-Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of (s,t)-Wythoff’s game, where a player is restricted to remove a multiple of K tokens in each move (K is a fixed positive integer). The others we called rook type restrictions of (s,t)-Wythoff’s game, including Odd-Arbitrary-Nim (s,t)-Wythoff’s Game, Odd–Odd-Nim (s,t)-Wythoff’s Game and Odd–Even-Nim (s,t)-Wythoff’s Game. In these three games, the restrictions are only made on horizontal and vertical moves, but not on the extended diagonal moves. For any K,s,t≥1, the sets of P-positions of our games are given in both normal and misère play.
Author Liu, Sanyang
Li, Haiyan
Fraenkel, Aviezri S.
Liu, Wen An
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10.1016/j.dam.2014.08.009
10.1016/j.disc.2011.03.032
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10.1080/00029890.1982.11995454
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10.1016/0097-3165(91)90070-W
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10.1016/j.disc.2005.06.022
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10.1109/CSO.2012.98
10.1016/j.jcta.2012.03.010
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Normal play convention
P-position
(s,t)-Wythoff’s game
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Snippet In this paper, we study four games, they are all restrictions of (s,t)-Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type...
In this paper, we study four games, they are all restrictions of (s, t)-Wythoff's game which was introduced by A.S. Fraenkel. The first one is a modular type...
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SubjectTerms [formula omitted]-position
[formula omitted]-Wythoff’s game
Applied mathematics
Combinatorics
Constrictions
Games
Normal play convention
Restriction
Title Variants of (s,t)-Wythoff’s game
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