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Prefix-free words of length N over M letters : two-sided well-balanced parentheses and palindroms

Part of the Lecture Notes in Mathematics book series (LNM,volume 1234)

Abstract

Prefix-free words of a given language L can be obtained within the frame of the classical problem of random words. If

is the number of prefix-free words of length n of L, we find here the functional equation verified by the generating function

of the

’s, and solve this problem with exact and asymptotic formulas, for two kinds of languages : the two-sided well-balanced parentheses over the alphabet A={a1, ... am, ā1, ām}, and the palindroms over A={a1, ... am}.

Keywords

  • Classical Problem
  • Formal Language Theory
  • Left Factor
  • Random Word
  • Minimum Modulus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1986 Springer-Verlag

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Beauquier, J., Thimonier, L. (1986). Prefix-free words of length N over M letters : two-sided well-balanced parentheses and palindroms. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072506

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  • DOI: https://doi.org/10.1007/BFb0072506

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17207-9

  • Online ISBN: 978-3-540-47402-9

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