Tokyo Journal of Mathematics

Maximal Determinant Knots

Alexander STOIMENOW

Full-text: Open access

Abstract

The Kauffman bracket approach is used to give estimates on the size of the determinant (and this way also on the coefficients of the Jones and Alexander polynomial) of a link of given crossing number, or equivalently on the number of spanning trees of planar graphs with given number of edges. Properties of the knots and links with maximal determinant for given crossing number are investigated.

Article information

Source
Tokyo J. Math., Volume 30, Number 1 (2007), 73-97.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1184963648

Digital Object Identifier
doi:10.3836/tjm/1184963648

Mathematical Reviews number (MathSciNet)
MR2328056

Zentralblatt MATH identifier
1131.57011

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 05A20: Combinatorial inequalities 57M12: Special coverings, e.g. branched

Citation

STOIMENOW, Alexander. Maximal Determinant Knots. Tokyo J. Math. 30 (2007), no. 1, 73--97. doi:10.3836/tjm/1184963648. https://projecteuclid.org/euclid.tjm/1184963648


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