Nonhomogeneous Beatty Sequences Leading to Invariant Games
نویسندگان
چکیده
We characterize pairs of complementary non-homogeneous Beatty sequences (An)n>0 and (Bn)n>0, with the restriction A1 = 1 and B1 ≥ 3, for which there exists an invariant take-away game having {(An, Bn), (Bn, An) | n > 0} ∪ {(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 [11].
منابع مشابه
Invariant games and non-homogeneous Beatty sequences
We characterize all the pairs of complementary non-homogenous Beatty sequences (An) n≥0 and (Bn) n≥0 for which there exists an invariant game having exactly {(An, Bn) | n ≥ 0} ∪ {(Bn, An) | n ≥ 0} as set of P-positions. Using the notion of Sturmian word and tools arising in symbolic dynamics and combinatorics on words, this characterization can be translated to a decision procedure relying only...
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 30 شماره
صفحات -
تاریخ انتشار 2016