On lazy representations and Sturmian graphs

Chiara Epifanio, Filippo Mignosi, Jeffrey Shallit, Christiane Frougny

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.
Original languageEnglish
Title of host publication15th International Conference, CIAA 2010
Pages125-134
Number of pages10
Volume6482
Publication statusPublished - 2011

Publication series

NameLECTURE NOTES IN COMPUTER SCIENCE

Fingerprint

Numeration System
Path
Graph in graph theory
Non-negative
Integer
Relationships

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Epifanio, C., Mignosi, F., Shallit, J., & Frougny, C. (2011). On lazy representations and Sturmian graphs. In 15th International Conference, CIAA 2010 (Vol. 6482, pp. 125-134). (LECTURE NOTES IN COMPUTER SCIENCE).

On lazy representations and Sturmian graphs. / Epifanio, Chiara; Mignosi, Filippo; Shallit, Jeffrey; Frougny, Christiane.

15th International Conference, CIAA 2010. Vol. 6482 2011. p. 125-134 (LECTURE NOTES IN COMPUTER SCIENCE).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Epifanio, C, Mignosi, F, Shallit, J & Frougny, C 2011, On lazy representations and Sturmian graphs. in 15th International Conference, CIAA 2010. vol. 6482, LECTURE NOTES IN COMPUTER SCIENCE, pp. 125-134.
Epifanio C, Mignosi F, Shallit J, Frougny C. On lazy representations and Sturmian graphs. In 15th International Conference, CIAA 2010. Vol. 6482. 2011. p. 125-134. (LECTURE NOTES IN COMPUTER SCIENCE).
Epifanio, Chiara ; Mignosi, Filippo ; Shallit, Jeffrey ; Frougny, Christiane. / On lazy representations and Sturmian graphs. 15th International Conference, CIAA 2010. Vol. 6482 2011. pp. 125-134 (LECTURE NOTES IN COMPUTER SCIENCE).
@inbook{eca0909decc24e4b918097b95fdfffae,
title = "On lazy representations and Sturmian graphs",
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.",
keywords = "numeration systems, Sturmian graphs, continued fractions",
author = "Chiara Epifanio and Filippo Mignosi and Jeffrey Shallit and Christiane Frougny",
year = "2011",
language = "English",
isbn = "978-3-642-18097-2",
volume = "6482",
series = "LECTURE NOTES IN COMPUTER SCIENCE",
pages = "125--134",
booktitle = "15th International Conference, CIAA 2010",

}

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 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.

AB - 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.

KW - numeration systems, Sturmian graphs, continued fractions

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

M3 - Chapter

SN - 978-3-642-18097-2

VL - 6482

T3 - LECTURE NOTES IN COMPUTER SCIENCE

SP - 125

EP - 134

BT - 15th International Conference, CIAA 2010

ER -

Access to Document