Article (Scientific journals)
Non-homogeneous Beatty sequences leading to invariant games
Cassaigne, Julien; Duchêne, Eric; Rigo, Michel
2016In SIAM Journal on Discrete Mathematics, 30, p. 1798-1829
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Keywords :
Two-player combinatorial game; Beatty sequence; Sturmian word; Invariant game; Superadditivity
Abstract :
[en] We characterize pairs of complementary non-homogeneous Beatty sequences $(A_n)_{n>0}$ and $(B_n)_{n>0}$, with the restriction $A_1=1$ and $B_1\geq 3$, for which there exists an invariant take-away game having $\{(A_n,B_n),(B_n,A_n)\mid n> 0\}\cup\{(0,0)\}$ as set of $P$-positions. Using the notion of Sturmian word arising in combinatorics on words, this characterization can be translated into a decision procedure relying only on a few algebraic tests about algebraicity or rational independence. This work partially answers to a question of Larsson et al. raised in Larsson et al.
Disciplines :
Mathematics
Author, co-author :
Cassaigne, Julien
Duchêne, Eric
Rigo, Michel  ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Non-homogeneous Beatty sequences leading to invariant games
Publication date :
2016
Journal title :
SIAM Journal on Discrete Mathematics
ISSN :
0895-4801
eISSN :
1095-7146
Publisher :
Society for Industrial & Applied Mathematics
Volume :
30
Pages :
1798-1829
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 03 June 2016

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