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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},
\end{displaymath} (1)

and satisfies
B_{\rm unknot} = q^{1/2}
\end{displaymath} (2)

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


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

© 1996-9 Eric W. Weisstein