The (s, t)-Wythoff's Game under Mis&amp;#x00E8;re Play Convention

Liu, Wen An; Wang, Yun; Li, Nali

doi:10.1109/cso.2012.98

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Under misère play convention, all P -positions of a-Wythoff's game were given in [13]. All P -positions of (s, t)-Wythoff's game were determined in [17], for all integers s, t 1.…”

Section: Extension Of Wythoff 'S Gamementioning

confidence: 99%

“…n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 B n 0 4 0 8 0 12 0 16 0 20 0 24 0 28 0 B n 1 5 1 9 1 13 1 17 1 21 1 25 1 29 1For s = t = 2, it follows from Table 7 that P 6 = (0, 0), (0, 1), (1,4), (1,5), (2, 0), (2,1), (3,8), (3,9), (4, 0), (4, 1), (5,12), (5,13), (6, 0), (6, 1), (7,16), (7,17), (8,…”

Section: Odd-even (S T)-wythoff 'S Gamementioning

confidence: 99%

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General Restriction of $(s,t)$-Wythoff's Game

Liu

2014

Electron. J. Combin.

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A.S. Fraenkel introduced a new $(s,t)$-Wythoff's game which is a generalization of both Wythoff's game and $a$-Wythoff's game. Four new models of a restricted version of $(s,t)$-Wythoff's game, Odd-Odd $(s,t)$-Wythoff's Game, Even-Even $(s,t)$-Wythoff's Game, Odd-Even $(s,t)$-Wythoff's Game and Even-Odd $(s,t)$-Wythoff's Game, are investigated. Under normal or misère play conventions, all $P$-positions of these four models are given for arbitrary integers $s,t\geq 1$. For Even-Even $(s,t)$-Wythoff's Game, the structure of $P$-positions is given by recursive characterizations in terms of the mex function. For other models, the structures of $P$-positions are of algebraic form, which permit us to decide in polynomial time whether or not a given game position $(a,b)$ is a $P$-position.

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“…Under misère play convention, all P -positions of a-Wythoff's game were given in [13]. All P -positions of (s, t)-Wythoff's game were determined in [17], for all integers s, t 1.…”

Section: Extension Of Wythoff 'S Gamementioning

confidence: 99%

Section: Odd-even (S T)-wythoff 'S Gamementioning

confidence: 99%

General Restriction of $(s,t)$-Wythoff's Game

Liu

2014

Electron. J. Combin.

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“…For examples, the a-Wythoff's game ( [5]), (s, t)-Wythoff's game ( [7]). Under normal and misère play conventions, the sets of all P -positions of the aWythoff's game and (s, t)-Wythoff's game are given in [5], [8], [12].…”

Section: Introductionmentioning

confidence: 99%

Preservation of P-Positions between a Game and Its Restricted Game

Liu

2014

2014 Seventh International Joint Conference on Computational Sciences and Optimization

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E. Duchêne et al investigate games whose sets of allowed moves are subsets of Wythoff's one, and whose set of P-positions is exactly Wythoff's sequence. Their results show that such a game does not exist. In this paper, we find a pair of games, one is the restricted version of the other, such that they have the same set of P-positions. We also find another pair of games, one is the restricted version of the other, such that they do not have the same set of P-positions. This means that the preservation of P-positions between a game and its restricted game depends on the game itself.

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Variants of(s,t)-Wythoff’s game

Liu

Fraenkel

et al. 2017

Discrete Applied Mathematics

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The (s, t)-Wythoff's Game under Misère Play Convention

Cited by 4 publications

References 15 publications

General Restriction of $(s,t)$-Wythoff's Game

General Restriction of $(s,t)$-Wythoff's Game

Preservation of P-Positions between a Game and Its Restricted Game

Variants of(s,t)-Wythoff’s game

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