Approximating algebraic functions by means of rational ones

In this paper, we use ECO method and the concept of succession rule to enumerate restricted classes of combinatorial objects. Let &O be the succession rule describing a construction of a combinatorial objects class, then the construction of the restricted class is described by means of an approximating succession rule ORk obtained from &O in a natural way. We give sufficient conditions for the rule k to be finite; finally we determine finite approximating rules for various classes of paths, and the approximation of the corresponding algebraic language with a regular one.

[1]  Julian West,et al.  Forbidden subsequences and Chebyshev polynomials , 1999, Discret. Math..

[2]  Mireille Bousquet-Mélou,et al.  Generating functions for generating trees , 2002, Discret. Math..

[3]  Elena Barcucci,et al.  Some combinatorial interpretations ofq-analogs of Schröder numbers , 1999 .

[4]  Alberto Del Lungo,et al.  ECO:a methodology for the enumeration of combinatorial objects , 1999 .

[5]  K. Chung,et al.  On fluctuations in coin tossing. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[6]  M. Aigner,et al.  Motzkin Numbers , 1998, Eur. J. Comb..

[7]  Fan Chung Graham,et al.  The Number of Baxter Permutations , 1978, J. Comb. Theory, Ser. A.

[8]  Julian West,et al.  Generating trees and the Catalan and Schröder numbers , 1995, Discret. Math..

[9]  Robert Donaghey,et al.  Motzkin Numbers , 1977, J. Comb. Theory, Ser. A.