Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-8sgpw Total loading time: 0.478 Render date: 2021-03-03T03:42:04.880Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Quasi-Sturmian colorings on regular trees

Published online by Cambridge University Press:  09 August 2019

DONG HAN KIM
Affiliation:
Department of Mathematics Education, Dongguk University–Seoul, 30 Pildong-ro 1-gil, Junggu, Seoul04620, Korea email kim2010@dongguk.edu
SEUL BEE LEE
Affiliation:
Department of Mathematical Sciences, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seulbee.lee@snu.ac.kr, deokwon.sim@snu.ac.kr
SEONHEE LIM
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seonhee.lim@gmail.com
DEOKWON SIM
Affiliation:
Department of Mathematical Sciences, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul08826, Korea email seulbee.lee@snu.ac.kr, deokwon.sim@snu.ac.kr

Abstract

Quasi-Sturmian words, which are infinite words with factor complexity eventually $n+c$ share many properties with Sturmian words. In this article, we study the quasi-Sturmian colorings on regular trees. There are two different types, bounded and unbounded, of quasi-Sturmian colorings. We obtain an induction algorithm similar to Sturmian colorings. We distinguish them by the recurrence function.

Type
Original Article
Copyright
© Cambridge University Press, 2019

Access options

Get access to the full version of this content by using one of the access options below.

References

Aberkane, A.. Words whose complexity satisfies limp (n)/n = 1. Theoret. Comput. Sci. 307(1) (2003), 3146.CrossRefGoogle Scholar
Allouche, J. and Shallit, J.. Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003.CrossRefGoogle Scholar
Cassaigne, J.. Sequences with grouped factors. Developments in Language Theory III (DLT’97). Aristotle University of Thessaloniki, Thessaloniki, 1998, pp. 211222.Google Scholar
Coven, E.. Sequences with minimal block growth. II. Math. Syst. Theory 8 (1974/75), 376382.CrossRefGoogle Scholar
Kim, D. H. and Lim, S.. Subword complexity and Sturmian colorings of regular trees. Ergod. Th. & Dynam. Sys. 35(2) (2015), 461481.CrossRefGoogle Scholar
Kim, D. H. and Lim, S.. Continued fraction algorithm for Sturmian colorings of trees. Ergod. Th. & Dynam. Sys. (published online in December 2017).Google Scholar
Lothaire, M.. Algebraic Combinatorics on Words (Encyclopedia of Mathematics and its Applications, 90). Cambridge University Press, Cambridge, 2002.CrossRefGoogle Scholar
Morse, M. and Hedlund, G.. Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62(1) (1940), 142.CrossRefGoogle Scholar
Paul, M.. Minimal symbolic flows having minimal block growth. Math. Syst. Theory 8 (1974/75), 309315.CrossRefGoogle Scholar
Pytheas Fogg, N.. Substitutions in Dynamics, Arithmetics and Combinatorics (Lecture Notes in Mathematics, 1794). Springer, Berlin, 2002.CrossRefGoogle Scholar
Rauzy, G.. Suites à termes dans un alphabet fini. Séminaire de théorie des nombres de Bordeaux, Exp. No 25, 1982–1983, 1–16.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 54 *
View data table for this chart

* Views captured on Cambridge Core between 09th August 2019 - 3rd March 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Quasi-Sturmian colorings on regular trees
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Quasi-Sturmian colorings on regular trees
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Quasi-Sturmian colorings on regular trees
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *