Enumerative sequences of leaves in rational trees

  • Frédérique Bassino
  • Marie-Pierre Béal
  • Dominique Perrin
Session 1: Formal Languages I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)


We prove that any IN-rational sequence s=(sn)n≥1 of non-negative integers satisfying the Kraft strict inequality \(\sum\nolimits_{n \geqslant 1} {s_n k^{ - n} } < 1\)is the enumerative sequence of leaves by height of a rational k-ary tree. Particular cases of this result had been previously proven. We give some partial results in the equality case.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Frédérique Bassino
    • 1
  • Marie-Pierre Béal
    • 2
  • Dominique Perrin
    • 1
  1. 1.Institut Gaspard MongeUniversité de Marne-la-ValléeFrance
  2. 2.Institut Gaspard MongeUniversité Paris 7 et CNRSFrance

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