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A morphic approach to combinatorial games: the Tribonacci case

Published online by Cambridge University Press:  13 December 2007

Eric Duchêne  and
Michel Rigo
Eric Duchêne
Affiliation:
Institute of Mathematics, University of Liège, Grande Traverse 12 (B37), 4000 Liège, Belgium; Eric.Duchene@ulg.ac.be; M.Rigo@ulg.ac.be
Michel Rigo
Affiliation:
Institute of Mathematics, University of Liège, Grande Traverse 12 (B37), 4000 Liège, Belgium; Eric.Duchene@ulg.ac.be; M.Rigo@ulg.ac.be
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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.

Keywords

Two-player combinatorial gamecombinatorics on wordsnumeration systemTribonacci sequence
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 375 - 393
Copyright
© EDP Sciences, 2007

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