6533b7defe1ef96bd1275f78

RESEARCH PRODUCT

On lazy representations and Sturmian graphs

Filippo MignosiChristiane FrougnyJeffrey ShallitChiara EpifanioAlessandra Gabriele

subject

Discrete mathematicsCombinatoricsOstrowski numerationIntegernumeration systems Sturmian graphs continued fractionsSettore INF/01 - InformaticaGraphMathematicsReal number

description

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.

yearjournalcountryeditionlanguage
2011-01-01
10.1007/978-3-642-18098-9_14http://hdl.handle.net/10447/60458