Reference : Extensions and restrictions of Wythoff's game preserving its P positions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Extensions and restrictions of Wythoff's game preserving its P positions
Duchêne, Eric [ > > ]
Fraenkel, Aviezri [ > > ]
Nowakowski, Richard [ > > ]
Rigo, Michel mailto [Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes >]
Journal of Combinatorial Theory. Series A
Academic Press
Yes (verified by ORBi)
[en] Wythoff's game ; game theory ; morphic word ; shape-symmetry ; automatic sequence ; fibonacci numeration system
[en] We consider extensions and restrictions of Wythoff's game having exactly the same set of P positions as the original game. No strict subset of rules give the same set of P positions. On the other hand, we characterize all moves that can be adjoined while preserving the original set of P positions. Testing if a move belongs to such an extended set of rules is shown to be doable in polynomial time. Many arguments rely on the infinite Fibonacci word, automatic sequences and the corresponding number system. With these tools, we provide new two-dimensional morphisms generating an infinite picture encoding respectively P positions of Wythoff's game and moves that can be adjoined.

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