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Enumeration of three kinds of rooted maps on the klein bottle

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Abstract

In this paper,\(\tilde 2\)-essential — essential rooted maps on the Klein bottle are counted and an explicit expression with the size as a parameter is given. Further, the numbers of singular maps and the maps with one vertex on the Klein bottle are derived.

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References

  1. D. Arquès,Relations fonctionelles et dénombremant des cartes pointées sur le tore, J. Comb. Theory, Series B43 (1987), 253–274.

    Article  MATH  Google Scholar 

  2. E. A. Bender, E. R. Canfield and R. W. Robinson,The enumeration of maps on the torus and the projective plane, Canada. Math. Bull.31 (1988), 257–271.

    MATH  MathSciNet  Google Scholar 

  3. W. G. Brown,On the enumeration of non-planar maps, Mem. Amer. Math. Soc.65 (1966).

  4. Zhicheng Gao,The number of rooted 2-connected triangular maps on the pojective plane, J. Comb. Theory, Series B53 (1991), 130–142.

    Article  MATH  Google Scholar 

  5. Rongxia Hao, Junliang Cai and Yanpei Liu,Counting g-essential maps with small genera, J. Appl. Math. & Computing (old:KJCAM)9(2) (2002), 451–463.

    MATH  MathSciNet  Google Scholar 

  6. Zhaoxiang Li and Yanpei Liu,Chromatic sums of singular maps on some surfaces, J. Appl. Math & Computing15(1–2) (2004), 157–172.

    Google Scholar 

  7. Yanpei Liu,Enumerative Theory of Maps, Kluwer, Dordrecht/Boston/London 1999.

    MATH  Google Scholar 

  8. Yanpei Liu,Theory of Counting Combinatorial Maps [in Chinese], Science Press, Beijing, 2001.

    Google Scholar 

  9. Yanpei Liu,Advances in Combinatorial Maps [in Chinese], Northern Jiaotong University Press, Beijing, 2003.

    Google Scholar 

  10. Han Ren and Yanpei Liu,4-regular maps on the Klein bottle J. Comb. Theory, Series B82 (2001), 118–137.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. T. Tutte,A census of planar triangulations, Canad. J. Math14 (1962), 21–38.

    MATH  MathSciNet  Google Scholar 

  12. W. T. Tutte,A census of slicings, Canad. J. Math14 (1962), 708–722.

    MATH  MathSciNet  Google Scholar 

  13. W. T. Tutte,A census of planar maps, Canad. J. Math15 (1963), 249–271.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Beijing JiaoTong University, 100044, Beijing, P. R. China

    Wenzhong Liu & Yanpei Liu

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  1. Wenzhong Liu
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  2. Yanpei Liu
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Correspondence to Wenzhong Liu.

Additional information

Supported by NNSFC under Grant 603730308 and 10571013.

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Liu, W., Liu, Y. Enumeration of three kinds of rooted maps on the klein bottle. J. Appl. Math. Comput. 24, 411–419 (2007). https://doi.org/10.1007/BF02832329

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  • DOI: https://doi.org/10.1007/BF02832329

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