View source for Brandt-Lickorish-Millett-Ho polynomial

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An invariant of non-oriented links in $\mathbf{R}^3$, invented at the beginning of 1985 [[#References|[a1]]], [[#References|[a2]]] and generalized by L.H. Kauffman (the [[Kauffman polynomial]]; cf. also [[Link]]).

It satisfies the four term skein relation for a Kauffman skein quadruple (cf. also [[Conway skein triple]])
$$
Q_{L_{+}}(z)  + Q_{L_{-}}(z) = z\left({ Q_{L_{0}}(z)  + Q_{L_{\infty}}(z) }\right)
$$
and is normalized to be $1$ for the trivial knot.

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240b.gif" />

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  R.D. Brandt,   W.B.R. Lickorish,   K.C. Millett,   "A polynomial invariant for unoriented knots and links"  ''Invent. Math.'' , '''84'''  (1986)  pp. 563–573</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  C.F. Ho,   "A new polynomial for knots and links; preliminary report"  ''Abstracts Amer. Math. Soc.'' , '''6''' :  4  (1985)  pp. 300</TD></TR>
</table>