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A class of extensions of Restricted (s,t)-Wythoff’s game

Sanyang Liu, Haiyan Li (2017)

Open Mathematics

Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

A morphic approach to combinatorial games : the Tribonacci case

Eric Duchêne, Michel Rigo (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

A morphic approach to combinatorial games: the Tribonacci case

Eric Duchêne, Michel Rigo (2007)

RAIRO - Theoretical Informatics and Applications

We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

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