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Families enumerated by the schröder-etherington sequence and a renewal array it generates

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1036)

Keywords

  • Legendre Polynomial
  • Universal Algebra
  • Combinatorial Interpretation
  • Symbol String
  • Catalan Sequence

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References

  1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, U.S. Government Printing Office, 1968.

    Google Scholar 

  2. A. Cayley, On the theory of the analytical forms called trees, Philosophical Magazine, 13 (1857) 172–176.

    Google Scholar 

  3. I.H.M. Etherington, some problems of non-associative combinations (1), Edinburgh Mathematical Notes 32 (1940) I–IV.

    CrossRef  Google Scholar 

  4. H.M. Finucan, Some decompositions of generalised Catalan Numbers, preprint to appear in the Proceedings of the Ninth Australian Conference of Combinatorial Mathematics.

    Google Scholar 

  5. I.J. Good, The generalisation of Lagrange's expansion and the enumeration of trees, Proc. Camb. Phil. Soc., 61(1965) 499–517.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S.G. Kettle, Every Catalan family is an Etherington family and vice versa, in preparation.

    Google Scholar 

  7. H. Lausch and W. Nöbauer, Algebra of Polynomials, North-Holland Publishing Co., London/New York, 1973.

    MATH  Google Scholar 

  8. G. Labelle, Une Nourelle démonstration combinatoire der formules d'inversion de Lagrange, Advances in Maths. 42(1981) 217–247.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. J.W. Moon, Counting labelled trees, Canadian Mathematical Monographs, 1970.

    Google Scholar 

  10. R.C. Mullin and R.G. Stanton, A map-theoretic approach to Davenport-Schinzel sequences, Pacific Journal of Mathematics (1) 40(1972) 167–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. G.N. Raney, Functional composition patterns and power series reversion, Trans. Am. Math. Soc., 94(1960), 441–451.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. D.G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Mathematics 22 (1978) 301–310.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. E. Schröder, Vier combinatorische Probleme, Zeitschrift für Mathematik und Physik, 15 (1870), 371–376.

    Google Scholar 

  14. N.J.A. Sloane, A handbook of integer sequences, Academic Press, New York, 1973.

    MATH  Google Scholar 

  15. G.N. Watterson, private communication.

    Google Scholar 

  16. J.G. Wendel, Left-continuous random walk and the Lagrange expansion, Am. Math. Monthly, 82 (1975) 494–499.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1983 Springer-Verlag

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Kettle, S.G. (1983). Families enumerated by the schröder-etherington sequence and a renewal array it generates. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071523

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  • DOI: https://doi.org/10.1007/BFb0071523

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12708-6

  • Online ISBN: 978-3-540-38694-0

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