Square Bracket Polynomial

A Polynomial which is not necessarily an invariant of a Link. It is related to the Dichroic Polynomial. It is defined by the Skein Relationship

$$B_{L_+}=q^{-1/2} v B_{L_0}+B_{L_\infty},$$ (1)

and satisfies

$$B_{\rm unknot} = q^{1/2}$$ (2)

and

$$B_{L\cup \rm unknot}=q^{1/2} B_L.$$ (3)

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 235-241, 1994.