Advertisement

Journal of Mathematical Sciences

, Volume 236, Issue 5, pp 521–526 | Cite as

Counting Unlabelled Chord Diagrams of Maximal Genus

  • E. KraskoEmail author
Article
  • 9 Downloads

We enumerate maximal chord diagrams up to all isomorphisms. The enumeration formula is based on a bijection between the rooted one-vertex one-face maps on locally orientable surfaces and a certain class of symmetric chord diagrams. This result extends the result of Cori and Marcus on the enumeration of maximal chord diagrams up to rotations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. R. S. Walsh and A. B. Lehman, “Counting rooted maps by genus,” J. Combin. Theory Ser. B, 13, 192–218 (1972).MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Harer and D. Zagier, “The Euler characteristic of the moduli space of curves,” Invent. Math., 85, 457–485 (1986).MathSciNetCrossRefGoogle Scholar
  3. 3.
    R. Cori and M. Marcus, “Counting non-isomorphic chord diagrams,” Theoret. Comput. Sci., 204, 55–73 (1998).MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. C. Read, “On general dissections of a polygon,” Aequationes Math., 18, 370–388 (1978).MathSciNetCrossRefGoogle Scholar
  5. 5.
    N. C. Wormald, “Counting unrooted planar maps,” Discrete Math., 36, 205–225 (1981).MathSciNetCrossRefGoogle Scholar
  6. 6.
    V. A. Liskovets, “A reductive technique for enumerating non-isomorphic planar maps,” Discrete Math., 156, 197–217 (1996).MathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Ledoux, “A recursion formula for the moments of the Gaussian orthogonal ensemble,” Ann. Inst. H. Poincaré Probab. Statist., 45, No. 3, 754–769 (2009).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Mednykh and R. Nedela, “Enumeration of unrooted maps of a given genus,” J. Combin. Theory Ser. B, 96, No. 5, 709–729 (2006).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg Academic UniversitySt. PetersburgRussia

Personalised recommendations