Brandt-Lickorish-Millett-Ho polynomial

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2010 Mathematics Subject Classification: Primary: 57M27 [MSN][ZBL]

An invariant of non-oriented links in $\mathbf{R}^3$, invented at the beginning of 1985 [a1], [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.


[a1] 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
[a2] C.F. Ho, "A new polynomial for knots and links; preliminary report" Abstracts Amer. Math. Soc. , 6 : 4 (1985) pp. 300


How to Cite This Entry:
Brandt-Lickorish-Millett-Ho polynomial. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Jozef Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article