2009, English, Article edition: Extensions and restrictions of Wyhtoff's game preserving Wythoff's P-positions Duchene, Eric; Fraenkel, Aviezri; Nowakowski, Richard J.; ...

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Physical Description
  • text
Published
  • HAL - CCSD
  • 2009
Language
  • English

Edition details

Title
  • Extensions and restrictions of Wyhtoff's game preserving Wythoff's P-positions
Author
  • Duchene, Eric
  • Fraenkel, Aviezri
  • Nowakowski, Richard J.
  • Rigo, Michel
Published
  • HAL - CCSD
  • 2009
Physical Description
  • text
Subjects
Notes
  • We consider extensions and restrictions of Wythoff's game having exactly the same set of $\PP$ positions as the original game. No strict subset of rules give the same set of $\PP$ positions. On the other hand, we characterize all moves that can be adjoined while preserving the original set of $\PP$ 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 $\PP$ positions of Wythoff's game and move that can be adjoined.
  • HAL:hal-00408012, version 1
  • HAL:http:/​/​hal.archives-ouvertes.fr/​hal-00408012/​en/​
Language
  • English
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