Distributions of regular branched surface coverings

  • Authors:

  • I. P. Goulden;Jin Ho Kwak;Jaeun Lee

  • Affiliations:

  • Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea;Mathematics, Yeungnam University, Kyongsan 712-749, Republic of Korea

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2004

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Abstract

In a study of surface branched coverings, one can ask naturally: In how many different ways can a given surface be a branched covering of another given surface? This problem was studied by many authors in Quart. J. Math. Oxford Ser. 2 46 (1995) 485, Math. Scand. 84 (1999) 23, Discrete Math. 156 (1996) 141, Discrete Math. 183 (1998) 193, Discrete Math. (in press), European J. Combin. 22 (2001) 1125, Sibirsk. Mat. Zh. 25 (1984) 606 etc. In this paper, as a complete answer to the question for regular coverings, we determine the distribution of the regular branched coverings of any nonorientable surface S when the covering transformation group and a set of branch points are freely assigned.