Skip to main content
SpringerLink
Log in

Simplification of formulas for the number of maps on surfaces

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

Two combinatorial identities obtained by the author are used to simplify formulas for the number of general rooted cubic planar maps, for the number of g-essential maps on surfaces of small genus, and also for rooted Eulerian maps on the projective plane. Besides, an asymptotics for the number of maps with a large number of vertices is obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. T. Tutte, “The enumerative theory of planar maps,” in A Survey of Combinatorial Theory, Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971 (North-Holland, Amsterdam, 1973), pp. 437–448.

    Google Scholar 

  2. E. A. Bender and L. B. Richmond, “A survey of the asymptotic behavior of maps,” J. Combin. Theory Ser. B 40(3), 297–329 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  3. Y. Liu, Enumerative Theory of Maps, in Mathematics and Its Applications (Kluwer Academic Publishers, Dordrecht, 1999), Vol. 468.

    Google Scholar 

  4. Y. Liu, “A note on the number of cubic planar maps,” Acta Math. Sci. 12(3), 282–285 (1992).

    MATH  MathSciNet  Google Scholar 

  5. R. Hao, Y. Cai, and Y. Liu, “Counting g-essential maps on surfaces with small genera,” Korean J. Comput. Appl. Math. 9(2), 451–463 (2002).

    MATH  MathSciNet  Google Scholar 

  6. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Elementary Functions (Fizmatlit, Moscow, 1981) [in Russian].

    MATH  Google Scholar 

  7. V. A. Voblyi, “Asymptotics of the number of cubic planar maps” Obozr. Prikl. Prom. Mat. 12(4), 850–851 (2005).

    Google Scholar 

  8. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1: The Hypergeometric Function, Legendre Functions (McGraw-Hill, New York-Toronto-London, 1953; Nauka-Fizmatlit, Moscow, 1965).

    Google Scholar 

  9. H.W. Gould, Combinatorial Identities: A Standardized Set of Tables Listing 500 Binomial Coefficient Summations (Morgentown, West Virginia Univ., 1972).

  10. V. A. Voblyi, “Simplification of formulas for the number of g-essential maps on the surfaces of small genus,” Obozr. Prikl. Prom. Mat. 11(2), 236–237 (2004).

    Google Scholar 

  11. H. Ren and Y. Liu, “Counting rooted Eulerian maps on the projective plane,” Acta Math. Sci. Ser. B 20(2), 169–174 (2000).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bauman State Technical University, Moscow, Russia

    V. A. Voblyi

Authors
  1. V. A. Voblyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V. A. Voblyi, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 1, pp. 14–23.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voblyi, V.A. Simplification of formulas for the number of maps on surfaces. Math Notes 83, 14–22 (2008). https://doi.org/10.1134/S0001434608010021

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434608010021

Key words

Search

Navigation