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A spanning tree expansion of the jones polynomial
A NEW combinatorial formulation of the Jones polynomial of a link is used to establish some basic properties of this polynomial. A striking consequence of these properties is the result that a linkExpand
Some links with non-trivial polynomials and their crossing-numbers
One of the main applications of the Jones polynomial invariant of oriented links has been in understanding links with (reduced, connected) alternating diagrams [2], [8], [9]. The Jones polynomial forExpand
Flexing closed hyperbolic manifolds.
We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in theExpand
The first 1,701,936 knots
inc lude all pr ime knots wi th 16 or fewer crossings. This r epresen t s more than a 130-fold increase in the number of t abu la ted knots s ince the last burs t of tabula t ion tha t t ook p laceExpand
Kauffman's polynomial and alternating links
These theorems result in quick tests which will often distinguish between links having alternating diagrams with the same number of crossings; links having reduced alternating diagrams with differentExpand
The rate of growth of the number of prime alternating links and tangles
When introduced to the subject of knot theory, it is natural to ask how the number of knots and links grows in relation to crossing number. The purpose of this article is to address this question forExpand
Classification of knot projections
Abstract The first step in tabulating the non-composite knots with n crossings is the tabulation of the non-singular plane projections of such knots, where two (piecewise linear) projections areExpand
The Tait flyping conjecture
We announce a proof of the Tait flyping conjecture; the confirmation of this conjecture renders almost trivial the problem of deciding whether two given alternating link diagrams represent equivalentExpand