Abstract
We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bašić, B.: On highly potential words. Eur. J. Combin. 34(6), 1028–1039 (2013)
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. Adv. Appl. Math. 47(3), 562–574 (2011)
Balková, L., Pelantová, E., Starosta, Š.: Proof of the Brlek-Reutenauer conjecture. Theoret. Comput. Sci. 475, 120–125 (2013)
Massé, A.B., Brlek, S., Frosini, A., Labbé, S., Rinaldi, S.: Reconstructing words from a fixed palindromic length sequence. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) TCS 2008. IIFIP, vol. 273, pp. 101–114. Springer, Boston, MA (2008). doi:10.1007/978-0-387-09680-3_7
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)
Blondin Massé, A., Brlek, S., Labbé, S., Vuillon, L.: Palindromic complexity of codings of rotations. Theoret. Comput. Sci. 412(46), 6455–6463 (2011)
Brlek, S., Reutenauer, C.: Complexity and palindromic defect of infinite words. Theoret. Comput. Sci. 412(4–5), 493–497 (2011)
Brlek, S., Hamel, S., Nivat, M., Reutenauer, C.: On the palindromic complexity of infinite words. Int. J. Found. Comput. Sci. 15(2), 293–306 (2004)
Bucci, M., Vaslet, E.: Palindromic defect of pure morphic aperiodic words. In: Proceedings of the 14th Mons Days of Theoretical Computer Science (2012)
Bucci, M., De Luca, A., Glen, A., Zamboni, L.Q.: A connection between palindromic and factor complexity using return words. Adv. Appl. Math. 42(1), 60–74 (2009)
Bucci, M., De Luca, A., Glen, A., Zamboni, L.Q.: A new characteristic property of rich words. Theoret. Comput. Sci. 410(30–32), 2860–2863 (2009)
Bucci, M., Luca, A., Luca, A.: Rich and periodic-like words. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 145–155. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02737-6_11
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)
Droubay, X., Pirillo, G.: Palindromes and Sturmian words. Theoret. Comput. Sci. 223(1–2), 73–85 (1999)
Glen, A., Justin, J., Widmer, S., Zamboni, L.Q.: Palindromic richness. Eur. J. Combin. 30(2), 510–531 (2009)
Guo, C., Shallit, J., Shur, A.M.: Palindromic rich words and run-length encodings. Inf. Process. Lett. 116(12), 735–738 (2016)
Harju, T., Vesti, J., Zamboni, L.Q.: On a question of Hof, Knill and Simon on palindromic substitutive systems. Monatsh. Math. 179(3), 379–388 (2016)
Hof, A., Knill, O., Simon, B.: Singular continuous spectrum for palindromic Schrödinger operators. Commun. Math. Phys. 174, 149–159 (1995)
Jajcayová, T., Pelantová, E., Starosta, Š.: Palindromic closures using multiple antimorphisms. Theoret. Comput. Sci. 533, 37–45 (2014)
Labbé, S., Pelantová, E.: Palindromic sequences generated from marked morphisms. Eur. J. Combin. 51, 200–214 (2016)
Labbé, S., Pelantová, E., Starosta, Š.: On the zero defect conjecture. Eur. J. Comb. 62, 132–146 (2017)
Labbé, S.: A counterexample to a question of Hof, Knill and Simon. Electron. J. Combin. 21 (2014). Paper #P3.11
de Luca, A., Glen, A., Zamboni, L.Q.: Rich, sturmian, and trapezoidal words. Theoret. Comput. Sci. 407(1), 569–573 (2008)
Masáková, Z., Pelantová, E., Starosta, Š.: Exchange of three intervals: substitutions and palindromicity. Eur. J. Combin. 62, 217–231 (2017)
Pelantová, E., Starosta, Š.: Languages invariant under more symmetries: overlapping factors versus palindromic richness. Discret. Math. 313, 2432–2445 (2013)
Pelantová, E., Starosta, Š.: Palindromic richness for languages invariant under more symmetries. Theor. Comput. Sci. 518, 42–63 (2014)
Pelantová, E., Starosta, Š.: Constructions of words rich in palindromes and pseudopalindromes. Discret. Math. Theoret. Comput. Sci. 18(3), 1–26 (2016)
Restivo, A., Rosone, G.: Balancing and clustering of words in the Burrows-Wheeler transform. Theoret. Comput. Sci. 412(27), 3019–3032 (2011)
Rukavicka, J.: On number of rich words (2017). Preprint available at arXiv:1701.07778
Starosta, Š.: Generalized Thue-Morse words and palindromic richness. Kybernetika 48(3), 361–370 (2012)
Starosta, Š.: Morphic images of episturmian words having finite palindromic defect. Eur. J. Combin. 51, 359–371 (2016)
Tan, B.: Mirror substitutions and palindromic sequences. Theoret. Comput. Sci. 389(1–2), 118–124 (2007)
Vesti, J.: Extensions of rich words. Theoret. Comput. Sci. 548, 14–24 (2014)
Acknowledgements
The authors acknowledge financial support by the Czech Science Foundation grant GAČR 13-03538S.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Pelantová, E., Starosta, Š. (2017). On Words with the Zero Palindromic Defect. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-66396-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66395-1
Online ISBN: 978-3-319-66396-8
eBook Packages: Computer ScienceComputer Science (R0)