ECO-Approximation of Algebraic Functions

  • Elisa Pergola
  • Renzo Pinzani
  • Simone Rinaldi
Conference paper


In this paper we use ECO method to enumerate restricted classes of combinatorial objects; if a succession rule Ω describes the construction of a class, then the restricted class can be described by means of an approximating succession rule Ω k obtained from Ω; we determine finite approximating rules for various classes of paths, and the approximation of the corresponding algebraic language with a regular one.


Regular Language Lattice Path Combinatorial Object Succession Rule Dyck Path 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Banderier, C., Bousquet-Mélou, M., Denise, A., Flajolet, P., Gardy, D., GouyouBeauchamps, D.: On generating functions of generating trees. Proceedings of 11th FPSAC (1999) 40–52Google Scholar
  2. 2.
    Barcucci, E., Del Lungo, A., Pergola, E.: Permutations with one forbidden subsequence of increasing length. Proceedings of 9th FPSAC (1997) 49–60Google Scholar
  3. 3.
    Barcucci, E., Del Lungo, A., Pergola, E., Pinzani, R.: ECO: a methodology for the Enumeration of Combinatorial Objects. Journal of Difference Equations and Applications 5 (1999) 435–490MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Barcucci, E., Del Lungo, A., Pergola, E., Pinzani, R.: Some combinatorial interpretations of q-analogs of Schröder numbers. Annals of Combinatorics 3 (1999) 173–192CrossRefGoogle Scholar
  5. 5.
    Barcucci, E., Del Lungo, A., Rinaldi, S., Frosini, P.: From rational functions to regular languages. (to appear)Google Scholar
  6. 6.
    Chow, T., West, J.: Forbidden sequences and Chebyshev polynomials. Discrete Mathematics 204 (1999) 119–128MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Chung, F. R. K., Graham, R. L., Hoggatt, V. E., Kleimann, The number of Baxter permutations. J. Combin. Theory A 24 (1978) 382–394MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Chung, F. R. K., Feller, On fluctuations in coin tossing. Proc. Nat. Acad. Sci. 35 (1949) 605–608MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Donaghey, R., Shapiro, Motzkin numbers. J.Combin.Theory A 23 (1977) 291–301MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Schröder, Vier combinatorische probleme. Z. für Math. Physik A15 (1870) 361–370Google Scholar
  11. 11.
    West, Generating trees and the Catalan and Schröder numbers. Discrete Mathematics 146 (1995) 247–262MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Elisa Pergola
    • 1
  • Renzo Pinzani
    • 1
  • Simone Rinaldi
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaFirenzeItaly

Personalised recommendations