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CHIARA EPIFANIO

On lazy representations and Sturmian graphs

  • Authors: Epifanio, C; Frougny, C; Gabriele, A; Mignosi, F; Shallit,J
  • Publication year: 2011
  • Type: Capitolo o Saggio (Capitolo o saggio)
  • Key words: numeration systems, Sturmian graphs, continued fractions
  • OA Link: http://hdl.handle.net/10447/60458

Abstract

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.