Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-5rkl9 Total loading time: 0.22 Render date: 2022-12-06T22:14:38.343Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Combinatoire de mots récurrents de complexité n+2

Published online by Cambridge University Press:  25 September 2007

Idrissa Kaboré
Affiliation:
Institut Sciences Exactes et Appliquées, Univ. polytech. de Bobo-Dioulasso, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso; ikaborei@yahoo.fr
Théodore Tapsoba
Affiliation:
École Supérieure d'Informatique, Univ. polytech. de Bobo-Dioulasso, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso; theo_tapsoba@univ-ouaga.bf
Get access

Abstract

Nous établissons quelques propriétés des mots sturmiens et classifions, ensuite, les mots infinis qui possèdent, pour tout entier naturel non nul n, exactement n+2 facteurs de longueur n. Nous définissons également la notion d'insertion k à k sur les mots infinis puis nous calculons la complexité des mots obtenus en appliquant cette notion aux mots sturmiens. Enfin nous étudions l'équilibre et la palindromie d'une classe particulière de mots de complexité n+2 que nous appelons mots quasi-sturmiens par insertion et que nous caractérisons à l'aide des vecteurs de Parikh.

Type
Research Article
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

P. Alessandri, Classification et représentation des mots de complexité n + 2. Rapport technique, Université Aix-Marseille II (1995).
P. Alessandri, Codage de rotations et basses complexités. Thèse, Université Aix-Marseille II (1996).
Allouche, J.-P., Sur la complexité des suites infinies. Bull. Belg. Math. Soc. Simon Stevin 1 (1994) 133143.
Allouche, J.-P., Baake, M., Cassaigne, J. et Damanik, D., Palindrome complexity. Theoret. Comput. Sci. 292 (2003) 931. CrossRef
Berthée, V., Fréquences des facteurs des suites sturmiennes. Theoret. Comput. Sci. 165 (1996) 295309. CrossRef
Cassaigne, J., Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 6788.
J. Cassaigne, Sequences with grouped factors, in Developments in Language Theory III (DLT'97), pp. 211–222, Aristotle University af Thessaloniki (1998).
Coven, E.M., Sequences with minimal block growth. Math. Syst. Theory 8 (1975) 376382. CrossRef
Coven, E.M. et Hedlund, G.A., Sequences with minimal block growth. Math. Syst. Theory 7 (1973) 138153. CrossRef
Didier, G., Caractérisation des N-écritures et application à l'étude des suites de complexité ultimement n + C ste. Theoret. Comput. Sci. 215 (1999) 3149. CrossRef
Droubay, X. et Pirillo, G., Palindromes and Sturmian words. Theoret. Comput. Sci. 223 (1999) 7385. CrossRef
S. Dulucq et D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm. Theoret. comput. Sci. 71 (1990) 381–400.
Ferenczi, S. et Mauduit, C., Transcendency of numbers with a low complexity expansion. J. Number Theory 67 (1997) 146161. CrossRef
A. Heinis, Arithmetics and combinatorics of words of low complexity. Ph.D. Thesis, University of Leiden (2001).
M. Lothaire, Algebraic combinatorics on words, vol. 90 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press (2002).
Mignosi, F. et Séébold, P., Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux 5 (1993) 221233. CrossRef
Morse, M. et Hedlund, G.A., Symbolic dynamics. Amer. J. Math. 60 (1938) 815866. CrossRef
M. Morse et G.A. Hedlund, Symbolic dynamics II: Sturmian trajectories. Amer. J. Math. 62 (1940) 1–42. CrossRef
Paul, M.E., Minimal symbolic flows having minimal block growth. Math. Syst. Theory 8 (1975) 309315. CrossRef
N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics. Lect. Notes Math. 1794 (2002).
G. Rauzy, Suites à termes dans un alphabet fini. Sémin. Théor. Nombres Bordeaux 25 (1982–1983) 1–16.

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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.

Combinatoire de mots récurrents de complexité n+2
Available formats
×

Save article to Dropbox

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Combinatoire de mots récurrents de complexité n+2
Available formats
×

Save article to Google Drive

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Combinatoire de mots récurrents de complexité n+2
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *