Reference : Non-homogeneous Beatty sequences leading to invariant games
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/197811
Non-homogeneous Beatty sequences leading to invariant games
English
Cassaigne, Julien []
Duchêne, Eric []
Rigo, Michel mailto [Université de Liège > Département de mathématique > Mathématiques discrètes >]
2016
SIAM Journal on Discrete Mathematics
Society for Industrial & Applied Mathematics
30
1798-1829
Yes (verified by ORBi)
International
0895-4801
1095-7146
[en] Two-player combinatorial game ; Beatty sequence ; Sturmian word ; Invariant game ; Superadditivity
[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.
Researchers
http://hdl.handle.net/2268/197811

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