Extensions and restrictions of Wythoff's game preserving its P positions

https://doi.org/10.1016/j.jcta.2009.07.010Get rights and content
Under an Elsevier user license
open archive

Abstract

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 gives 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 numeration 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.

Keywords

Combinatorial game theory
Wythoff's game
Complexity of games
Automatic sequences
Numeration systems

Cited by (0)