Complexity of sequences defined by billiard in the cube

Pierre Arnoux; Christian Mauduit; Iekata Shiokawa; Jun-Ichi Tamura

Displaying similar documents to “Complexity of sequences defined by billiard in the cube”

Complexity and growth for polygonal billiards

J. Cassaigne, Pascal Hubert, Serge Troubetzkoy (2002)

Annales de l’institut Fourier

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We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.

Algebraic tools for the construction of colored flows with boundary constraints

Marius Dorkenoo, Marie-Christine Eglin-Leclerc, Eric Rémila (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We give a linear time algorithm which, given a simply connected figure of the plane divided into cells, whose boundary is crossed by some colored inputs and outputs, produces non-intersecting directed flow lines which match inputs and outputs according to the colors, in such a way that each edge of any cell is crossed by at most one line. The main tool is the notion of height function, previously introduced for tilings. It appears as an extension of the notion of potential of a flow...