6533b7d4fe1ef96bd1262096
RESEARCH PRODUCT
A Characterization of Bispecial Sturmian Words
Gabriele Ficisubject
CombinatoricsChristoffel symbolsApproximations of πEuclidean geometrySturmian wordAlphabetMathematicsSturmian words Christoffel words special factors minimal forbidden words enumerative formuladescription
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 |