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A morphic approach to combinatorial games: the Tribonacci case

Published online by Cambridge University Press:  13 December 2007

Eric Duchêne
Affiliation:
Institute of Mathematics, University of Liège, Grande Traverse 12 (B37), 4000 Liège, Belgium; [email protected]; [email protected]
Michel Rigo
Affiliation:
Institute of Mathematics, University of Liège, Grande Traverse 12 (B37), 4000 Liège, Belgium; [email protected]; [email protected]
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Abstract

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
Research Article
Copyright
© EDP Sciences, 2007

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