Subword complexity and projection bodies |
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Authors: | Christian Steineder |
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Institution: | Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria |
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Abstract: | A polytope P⊆0,1d) and an induce a so-called Hartman sequence which is by definition 1 at the kth position if and 0 otherwise, k∈Z. We prove an asymptotic formula for the subword complexity of such a Hartman sequence. This result establishes a connection between symbolic dynamics and convex geometry: If the polytope P is convex then the subword complexity of asymptotically equals the volume of the projection body ΠP of P for almost all . |
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Keywords: | 11K31 37B10 52B11 |
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