Words and morphisms with Sturmian erasures

Details Words and morphisms with Sturmian erasures Words and morphisms with Sturmian erasures

2008-01-03

arxiv.org/abs/0801.0558v1

Bulletin of the Belgian Mathematical Society 11, 4 (2004) 575-588

Mathematics

Combinatorics

Scientific paper

We say $x \in \{0,1,2 \}^{\NN}$ is a word with Sturmian erasures if for any $a\in \{0,1,2 \}$ the word obtained erasing all $a$ in $x$ is a Sturmian word. A large family of such words is given coding trajectories of balls in the game of billiards in the cube. We prove that the monoid of morphisms mapping all words with Sturmian erasures to words with Sturmian erasures is not finitely generated.

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