Tokyo Journal of Mathematics

Maximal Determinant Knots


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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

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

First available in Project Euclid: 20 July 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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