A morphic approach to combinatorial games : the Tribonacci case

Eric Duchêne; Michel Rigo

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

  • Volume: 42, Issue: 2, page 375-393
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Duchêne, Eric, and Rigo, Michel. "A morphic approach to combinatorial games : the Tribonacci case." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.2 (2008): 375-393. <http://eudml.org/doc/246096>.

@article{Duchêne2008,
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.},
author = {Duchêne, Eric, Rigo, Michel},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {two-player combinatorial game; combinatorics on words; numeration system; Tribonacci sequence},
language = {eng},
number = {2},
pages = {375-393},
publisher = {EDP-Sciences},
title = {A morphic approach to combinatorial games : the Tribonacci case},
url = {http://eudml.org/doc/246096},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Duchêne, Eric
AU - Rigo, Michel
TI - A morphic approach to combinatorial games : the Tribonacci case
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2008
PB - EDP-Sciences
VL - 42
IS - 2
SP - 375
EP - 393
AB - 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.
LA - eng
KW - two-player combinatorial game; combinatorics on words; numeration system; Tribonacci sequence
UR - http://eudml.org/doc/246096
ER -

References

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