| Issue |
RAIRO-Theor. Inf. Appl.
Volume 42, Number 2, April-June 2008
|
|
|---|---|---|
| Page(s) | 375 - 393 | |
| DOI | https://doi.org/10.1051/ita:2007039 | |
| Published online | 13 December 2007 | |
A morphic approach to combinatorial games: the Tribonacci case
Institute of Mathematics,
University of Liège, Grande Traverse 12 (B37),
4000 Liège, Belgium;
Eric.Duchene@ulg.ac.be;
M.Rigo@ulg.ac.be
Received:
7
May
2007
Accepted:
26
September
2007
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.
Mathematics Subject Classification: 91A46 / 68R15 / 68Q45
Key words: Two-player combinatorial game / combinatorics on words / numeration system / Tribonacci sequence
© EDP Sciences, 2007
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