Seifert circles and knot polynomials

H. R. Morton
1986 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial P K defined in [3] . The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case. Notation. In a diagram D for an oriented knot, write c + (D) and c~(D) for the number \ / of positive and negative crossings, where V is a positive crossing.
more » ... is a positive crossing.
doi:10.1017/s0305004100063982 fatcat:z3tbebpqujbytipl22up42bc6y