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Counting alternating knots by genus

Lookup NU author(s): Dr Alina Vdovina

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Abstract

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. © Springer-Verlag 2005.

Publication metadata

Author(s): Stoimenow A, Vdovina A

Publication type: Article

Publication status: Published

Journal: Mathematische Annalen

Year: 2005

Volume: 333

Issue: 1

Pages: 1-27

ISSN (print): 0025-5831

ISSN (electronic): 1432-1807

Publisher: Springer

URL: http://dx.doi.org/10.1007/s00208-005-0659-x

DOI: 10.1007/s00208-005-0659-x

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