0000000000425181

AUTHOR

Christiane Frougny

showing 2 related works from this author

On lazy representations and Sturmian graphs

2011

In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.

Discrete mathematicsCombinatoricsOstrowski numerationIntegernumeration systems Sturmian graphs continued fractionsSettore INF/01 - InformaticaGraphMathematicsReal number
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Sturmian graphs and integer representations over numeration systems

2012

AbstractIn this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural integers in this numeration system is regular if and only if the continued fraction expansion of α is eventually periodic. The main result of the paper is that for any number i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ost…

Discrete mathematicsContinued fractionsApplied MathematicsNumeration systemsSturmian graphsGraphCombinatoricsOstrowski numerationIntegerIf and only ifnumeration systems Sturmian graphs continued fractions.Numeration systems; SUBWORD GRAPHS; WORDSDiscrete Mathematics and CombinatoricsSUBWORD GRAPHSContinued fractionWORDSMathematicsReal number
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