6533b82cfe1ef96bd12900dd

RESEARCH PRODUCT

Sturmian graphs and integer representations over numeration systems

Filippo MignosiChiara EpifanioChristiane FrougnyJeffrey ShallitAlessandra Gabriele

subject

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

description

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 Ostrowski numeration system associated with α.

yearjournalcountryeditionlanguage
2012-03-01
10.1016/j.dam.2011.10.029http://hdl.handle.net/10447/62751