A morphic approach to combinatorial games: the Tribonacci case

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.

• Type: Journal
• Year: 2008
• Where: ITA
• Authors: Éric Duchêne, Michel Rigo
• Keywords: Communications, Corresponding Exotic Numeration, Game, ITA 2008, Piles Game