Geodesic
A geometrical approach of palindromic factors of standard billiard words
Discrete mathematics & theoretical computer science, Tome 9 (2007) no. 2.

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Many results are already known, concerning the palindromic factors and the palindomic prefixes of Standard billiard words, i.e., Sturmian words and billiard words in any dimension, starting at the origin. We give new geometrical proofs of these results, especially for the existence in any dimension of Standard billiard words with arbitrary long palindromic prefixes. 
@article{DMTCS_2007_9_2_a12,
     author = {Borel, Jean-Pierre},
     title = {A geometrical approach of palindromic factors of standard billiard words},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2007},
     doi = {10.46298/dmtcs.410},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.410/}
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Borel, Jean-Pierre. A geometrical approach of palindromic factors of standard billiard words. Discrete mathematics & theoretical computer science, Tome 9 (2007) no. 2. doi : 10.46298/dmtcs.410. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.410/

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