A morphic approach to combinatorial games: the Tribonacci case

Eric Duchene (1) , Michel Rigo (2)

1 LIESP - Laboratoire d'Informatique pour l'Entreprise et les Systèmes de Production
2 Université de Liège

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.

Mots clés: combinatorial game; combinatorics on words

Domaines: Mathématique discrète [cs.DM]

Eric Duchene, Michel Rigo. A morphic approach to combinatorial games: the Tribonacci case. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42, pp.375-393. ⟨hal-00408007⟩