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Enumerative sequences of leaves in rational trees

  • Session 1: Formal Languages I
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

We prove that any IN-rational sequence s=(s n )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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Author information

Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne-la-Vallée, France

    Frédérique Bassino & Dominique Perrin

  2. Institut Gaspard Monge, Université Paris 7 et CNRS, France

    Marie-Pierre Béal

Authors
  1. Frédérique Bassino
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  2. Marie-Pierre Béal
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  3. Dominique Perrin
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Bassino, F., Béal, MP., Perrin, D. (1997). Enumerative sequences of leaves in rational trees. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_166

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  • DOI: https://doi.org/10.1007/3-540-63165-8_166

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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