On lazy representations and Sturmian graphs

Chiara Epifanio; Filippo Mignosi; Jeffrey Shallit; Christiane Frougny

On lazy representations and Sturmian graphs

Chiara Epifanio, Filippo Mignosi, Jeffrey Shallit, Christiane Frougny

Matematica e Informatica

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Abstract

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

Original language	English
Title of host publication	15th International Conference, CIAA 2010
Pages	125-134
Number of pages	10
Publication status	Published - 2011

Publication series

Name	LECTURE NOTES IN COMPUTER SCIENCE

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Cite this

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title = "On lazy representations and Sturmian graphs",

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

keywords = "Sturmian graphs, continued fractions, numeration systems, Sturmian graphs, continued fractions, numeration systems",

author = "Chiara Epifanio and Filippo Mignosi and Jeffrey Shallit and Christiane Frougny",

year = "2011",

language = "English",

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TY - CHAP

T1 - On lazy representations and Sturmian graphs

AU - Epifanio, Chiara

AU - Mignosi, Filippo

AU - Shallit, Jeffrey

AU - Frougny, Christiane

PY - 2011

Y1 - 2011

N2 - In this paper we establish a strong relationship between theset of lazy representations and the set of paths in a Sturmian graph associatedwith a real number α. We prove that for any non-negative integeri the unique path weighted i in the Sturmian graph associated with αrepresents the lazy representation of i in the Ostrowski numeration systemassociated with α. Moreover, we provide several properties of therepresentations of the natural integers in this numeration system.

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

KW - Sturmian graphs

KW - continued fractions

KW - numeration systems

KW - Sturmian graphs

KW - continued fractions

KW - numeration systems

UR - http://hdl.handle.net/10447/60458

M3 - Chapter

SN - 978-3-642-18097-2

T3 - LECTURE NOTES IN COMPUTER SCIENCE

SP - 125

EP - 134

BT - 15th International Conference, CIAA 2010

ER -

On lazy representations and Sturmian graphs

Abstract

Publication series

All Science Journal Classification (ASJC) codes

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