Mathematische Annalen

, Volume 333, Issue 1, pp 1–27

Counting alternating knots by genus


DOI: 10.1007/s00208-005-0659-x

Cite this article as:
Stoimenow, A. & Vdovina, A. Math. Ann. (2005) 333: 1. doi:10.1007/s00208-005-0659-x


It is shown that the number of alternating knots of given genus g>1 grows as a polynomial of degree 6g−4 in the crossing number. The leading coefficient of the polynomial, which depends on the parity of the crossing number, is related to planar trivalent graphs with a Bieulerian path. The rate of growth of the number of such graphs is estimated.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan
  2. 2.School of Mathematics and StatisticsUniversity of NewcastleNewcastle upon TyneUK