6533b827fe1ef96bd1285df6

RESEARCH PRODUCT

On Sturmian Graphs

Ilaria VenturiniFilippo MignosiJeffrey ShallitChiara Epifanio

subject

Discrete mathematicsApplied MathematicsCDAWGsContinued fractionsSturmian wordSturmian wordsCharacterization (mathematics)RepeatsDirected acyclic graphCombinatoricsIndifference graphSturmian words CDAWGs Continued fractions RepeatsChordal graphComputer Science::Discrete MathematicsDiscrete Mathematics and CombinatoricsContinued fractionWord (group theory)Computer Science::Formal Languages and Automata TheoryReal numberMathematics

description

AbstractIn this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.

yearjournalcountryeditionlanguage
2007-04-01
http://hdl.handle.net/11697/18868