Rich and Periodic-Like Words (original) (raw)

Abstract

In this paper we investigate the periodic structure of rich words (i.e., words having the highest possible number of palindromic factors), giving new results relating them with periodic-like words. In particular, some new characterizations of rich words and rich palindromes are given. We also prove that a periodic-like word is rich if and only if the square of its fractional root is also rich.

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References (16)

  1. Droubay, X., Justin, J., Pirillo, G.: Episturmian words and some constructions of de Luca and Rauzy. Theoretical Computer Science 255 (2001) 539-553
  2. Allouche, J.P., Baake, M., Cassaigne, J., Damanik, D.: Palindrome complexity. Theoretical Computer Science 292 (2003) 9-31
  3. Ambrož, P., Frougny, C., Masáková, Z., Pelantová, E.: Palindromic complexity of infinite words associated with simple Parry numbers. Ann. Inst. Fourier (Grenoble) 56 (2006) 2131-2160
  4. Glen, A., Justin, J., Widmer, S., Zamboni, L.Q.: Palindromic richness. European Journal of Combinatorics 30 (2009) 510-531
  5. Bucci, M., De Luca, A., Glen, A., Zamboni, L.Q.: A connection between palin- dromic and factor complexity using return words. Advances in Applied Mathe- matics 42 (2009) 60-74
  6. de Luca, A., Glen, A., Zamboni, L.Q.: Rich, Sturmian, and trapezoidal words. Theoretical Computer Science 407 (2008) 569-573
  7. Bucci, M., De Luca, A., Glen, A., Zamboni, L.Q.: A new characteristic property of rich words. Theoretical Computer Science (to appear) (2009) doi:10.1016/j.tcs.2008.11.001.
  8. Carpi, A., de Luca, A.: Periodic-like words, periodicity, and boxes. Acta Informat- ica 37 (2001) 597-618
  9. Carpi, A., de Luca, A.: Semiperiodic words and root-conjugacy. Theoretical Com- puter Science 292 (2003) 111-130
  10. Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading MA (1983) Reprinted by Cambridge University Press, Cambridge UK, 1997.
  11. Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press (2002)
  12. de Luca, A.: On the combinatorics of finite words. Theoretical Computer Science 218 (1999) 13-39
  13. D'Alessandro, F.: A combinatorial problem on trapezoidal words. Theoretical Computer Science 273 (2002) 11-33
  14. de Luca, A., De Luca, A.: Combinatorial properties of Sturmian palindromes. International Journal of Foundations of Computer Science 17 (2006) 557-574
  15. Berstel, J.: Sturmian and Episturmian Words (a survey of some recent results). In Bozapalidis, S., Rahonis, G., eds.: Conference on Algebraic Informatics, Thes- saloniki. Volume 4728 of Lecture Notes in Computer Science. (2007) 23-47
  16. de Luca, A., De Luca, A.: Pseudopalindrome closure operators in free monoids. Theoretical Computer Science 362 (2006) 282-300