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Tiling and local rank properties of the Morse sequence. (English) Zbl 0820.68092
Summary: We study some combinatoric properties of the Morse sequence, linked with its ergodic properties of local rank one and local funny rank one; we show that the maximum part of the Morse sequence that may be covered by disjoint translates of one word is exactly of density 2/3, even allowing for some errors in the tiling; when we replace words by patterns (words with holes), 2/3 can be replaced by at least 5/6.

MSC:
68R15 Combinatorics on words
Keywords:
Morse sequence
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