Geodesic
A morphic approach to combinatorial games : the Tribonacci case
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 375-393

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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.

DOI : 10.1051/ita:2007039
Classification : 91A46, 68R15, 68Q45
Keywords: two-player combinatorial game, combinatorics on words, numeration system, Tribonacci sequence 
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     author = {Duch\^ene, Eric and Rigo, Michel},
     title = {A morphic approach to combinatorial games : the {Tribonacci} case},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {375--393},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/ita:2007039},
     mrnumber = {2401268},
     zbl = {1143.91314},
     language = {en},
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Duchêne, Eric; Rigo, Michel. A morphic approach to combinatorial games : the Tribonacci case. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 375-393. doi: 10.1051/ita:2007039

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