Tiling and local rank properties of the Morse sequence

AbstractWe 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 23, even allowing for some errors in the tiling; when we replace words by patterns (words with holes), 23 can be replaced by at least 56