Abstract
In this paper we consider the avoidance of patterns in infinite words. Generalising the traditional problem setting, functional dependencies between pattern variables are allowed here, in particular, patterns involving permutations. One of the remarkable facts is that in this setting the notion of avoidability index (the smallest alphabet size for which a pattern is avoidable) is meaningless since a pattern with permutations that is avoidable in one alphabet can be unavoidable in a larger alphabet. We characterise the (un-)avoidability of all patterns of the form π i(x) π j(x) π k(x), called cubes under permutations here, for all alphabet sizes in both the morphic and antimorphic case.
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.
Similar content being viewed by others
References
Bischoff, B., Nowotka, D.: Pattern avoidability with involution. In: Words 2011, Prague. Electron. Proc. in Theoret. Comput. Sci, vol. 63, pp. 65–70 (2011)
Cassaigne, J.: Unavoidable Patterns. In: Algebraic Combinatorics on Words, pp. 111–134. Cambridge University Press, Cambridge (2002)
Chiniforooshan, E., Kari, L., Xu, Z.: Pseudopower avoidance. Fundamenta Informaticae 114, 1–18 (2012)
Currie, J.: Pattern avoidance: themes and variations. Theoret. Comput. Sci. 339(1), 7–18 (2005)
Currie, J.: Pattern avoidance with involution. CoRR abs/1105.2849 (2011)
Hall, M.: Generators and relations in groups – The Burnside problem. In: Lectures on Modern Mathematics, vol. 2, pp. 42–92. Wiley, New York (1964)
Lothaire, M.: Combinatorics on Words. Cambridge University Press (1997)
Thue, A.: Über unendliche Zeichenreihen. Norske Vid. Skrifter I.,Mat.-Nat.,Kl., Christiania 7, 1–22 (1906)
Thue, A.: Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Skrifter I.,Mat.-Nat.,Kl., Christiania 1, 1–67 (1912)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manea, F., Müller, M., Nowotka, D. (2012). The Avoidability of Cubes under Permutations. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-31653-1_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31652-4
Online ISBN: 978-3-642-31653-1
eBook Packages: Computer ScienceComputer Science (R0)