Abstract
We focus on Θ-rich and almost Θ-rich words over a finite alphabet \(\mathcal{A}\), where Θ is an involutive antimorphism over \(\mathcal{A}^*\). We show that any recurrent almost Θ-rich word u is an image of a recurrent Θ′-rich word under a suitable morphism, where Θ′ is again an involutive antimorphism. Moreover, if the word u is uniformly recurrent, we show that Θ′ can be set to the reversal mapping. We also treat one special case of almost Θ-rich words. We show that every Θ-standard word with seed is an image of an Arnoux-Rauzy word.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anne, V., Zamboni, L.Q., Zorca, I.: Palindromes and pseudo-palindromes in episturmian and pseudo-episturmian infinite words. In: Brlek, S., Reutenauer, C. (eds.) Words 2005, vol. (36), pp. 91–100. LACIM (2005)
Baláži, P., Masáková, Z., Pelantová, E.: Factor versus palindromic complexity of uniformly recurrent infinite words. Theoret. Comput. Sci. 380(3), 266–275 (2007)
Balková, L., Pelantová, E., Starosta, Š.: Infinite words with finite defect. To appear in Adv. Appl. Math., (2011), preprint available at http://arxiv.org/abs/1009.5105
Blondin Massé, A., Brlek, S., Garon, A., Labbé, S.: Combinatorial properties of f-palindromes in the Thue-Morse sequence. Pure Math. Appl. 19(2-3), 39–52 (2008)
Brlek, S., Hamel, S., Nivat, M., Reutenauer, C.: On the palindromic complexity of infinite words. Internat. J. Found. Comput. 15(2), 293–306 (2004)
Bucci, M., De Luca, A.: On a family of morphic images of arnoux-rauzy words. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 259–266. Springer, Heidelberg (2009)
Bucci, M., De Luca, A., Glen, A., Zamboni, L.Q.: A connection between palindromic and factor complexity using return words. Adv. in Appl. Math. 42(1), 60–74 (2009)
Bucci, M., de Luca, A., De Luca, A.: Characteristic morphisms of generalized episturmian words. Theor. Comput. Sci. 410, 2840–2859 (2009)
Bucci, M., de Luca, A., De Luca, A.: Rich and periodic-like words. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 145–155. Springer, Heidelberg (2009)
Bucci, M., de Luca, A., De Luca, A., Zamboni, L.Q.: On different generalizations of episturmian words. Theoret. Comput. Sci. 393(1-3), 23–36 (2008)
Bucci, M., de Luca, A., De Luca, A., Zamboni, L.Q.: On theta-episturmian words. European J. Combin. 30(2), 473–479 (2009)
Droubay, X., Justin, J., Pirillo, G.: Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci. 255(1-2), 539–553 (2001)
Glen, A., Justin, J., Widmer, S., Zamboni, L.Q.: Palindromic richness. European J. Combin. 30(2), 510–531 (2009)
Hof, A., Knill, O., Simon, B.: Singular continuous spectrum for palindromic Schrödinger operators. Comm. Math. Phys. 174, 149–159 (1995)
Kari, L., Magalingam, K.: Watson-Crick palindromes in DNA computing. Nat. Comput. (9), 297–316 (2010)
Pelantová, E., Starosta, Š.: Languages invariant under more symmetries: overlapping factors versus palindromic richness. (2011), preprint available at http://arxiv.org/abs/1103.4051
Rauzy, G.: Suites à termes dans un alphabet fini. Séminaire de Théorie des Nombres de Bordeaux Anné 1982–1983(exposé 25) (1983)
Starosta, Š.: On theta-palindromic richness. Theoret. Comput. Sci. 412(12-14), 1111–1121 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pelantová, E., Starosta, Š. (2011). Infinite Words Rich and Almost Rich in Generalized Palindromes. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-22321-1_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22320-4
Online ISBN: 978-3-642-22321-1
eBook Packages: Computer ScienceComputer Science (R0)