Article (Scientific journals)
Cubic Pisot Unit Combinatorial Games
Duchêne, Eric; Rigo, Michel
2008In Monatshefte für Mathematik, 155, p. 217-249
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Keywords :
numeration system; Combinatorial game; morphic word; Pisot number; Tribonacci word
Abstract :
[en] Generalized Tribonacci morphisms are de ned on a three letters alphabet and generate the so-called generalized Tribonacci words. We present a family of combinatorial removal games on three piles of tokens whose set of P-positions is coded exactly by these generalized Tribonacci words. To obtain this result, we study combinatorial properties of these words like gaps between consecutive identical letters or recursive de nitions of these words. Beta-numeration systems are then used to show that these games are tractable, i.e., deciding whether a position is a P-position can be checked in polynomial time.
Disciplines :
Mathematics
Author, co-author :
Duchêne, Eric
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Cubic Pisot Unit Combinatorial Games
Publication date :
2008
Journal title :
Monatshefte für Mathematik
ISSN :
0026-9255
eISSN :
1436-5081
Publisher :
Springer
Volume :
155
Pages :
217-249
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 01 July 2009

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