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EJC
2016

Complexity of short rectangles and periodicity

7 years 12 months ago
Complexity of short rectangles and periodicity
The Morse-Hedlund Theorem states that a bi-infinite sequence η in a finite alphabet is periodic if and only if there exists n ∈ N such that the block complexity function Pη(n) satisfies Pη(n) ≤ n. In dimension two, Nivat conjectured that if there exist n, k ∈ N such that the n × k rectangular complexity Pη(n, k) satisfies Pη(n, k) ≤ nk, then η is periodic. Sander and Tijdeman showed that this holds for k ≤ 2. We generalize their result, showing that Nivat’s Conjecture holds for k ≤ 3. The method involves translating the combinatorial problem to a question about the nonexpansive subspaces of a certain Z2 dynamical system, and then analyzing the resulting system.
Van Cyr, Bryna Kra
Added 02 Apr 2016
Updated 02 Apr 2016
Type Journal
Year 2016
Where EJC
Authors Van Cyr, Bryna Kra
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