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Algebraic Generating Functions in Enumerative Combinatorics and Context-Free Languages

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STACS 2005 (STACS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3404))

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Abstract

Numerous families of simple discrete objects (words, trees, lattice walks...) are counted by a rational or algebraic generating function. Whereas it seems that objects with a rational generating function have a structure very similar to the structure of words of a regular language, objects with an algebraic generating function remain more mysterious. Some of them, of course, exhibit a clear “algebraic” structure, which recalls the structure of words of context-free languages. For many other objects, such a structure has not yet been discovered. We list several examples of this type, and discuss various methods for proving the algebraicity of a generating function.

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Author information

Authors and Affiliations

  1. CNRS, LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405 Cedex, Talence, France

    Mireille Bousquet-Mélou

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  1. Mireille Bousquet-Mélou
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Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIF, CNRS & Univ. de Provence,, Marseille

    Bruno Durand

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Bousquet-Mélou, M. (2005). Algebraic Generating Functions in Enumerative Combinatorics and Context-Free Languages. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-31856-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24998-6

  • Online ISBN: 978-3-540-31856-9

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