Polynomial invariants of positive links (Q1209389)

An oriented link \(L\subset R^ 3\) is called positive if \(L\) has a diagram \(D\subset R^ 2\) with no negative crossings. These links have nice properties to which the author adds one more and this is a correspondence in Kauffman and skein polynomials which are denoted \(F_ L(a,z)\) and \(P_ L(a,z)\), respectively. The result is the following: Assume \(D\) is a positive diagram of a positive link \(L\) and write \(F_ L(a,z)=\sum_ i F_ i(z;L)a^ i\), \(P_ L(a,z)=\sum_ i P_ i(z;L)a^ i\), where \(F_ i\)'s and \(P_ i\)'s are polynomials in \(z^{\pm 1}\). Then for \(i\geq s(D)-c_ +(D)-1\) it holds \(F_ i(z;L)=P_ i(z;L)\), where \(s(D)\) is the number of Seifert circles in \(D\) and \(c_ +(D)\) the number of positive crossings.