Let be the largest and the smallest Power of in the HOMFLY Polynomial of an oriented Link,
and be the Braid Index. Then the Morton-Franks-Williams Inequality holds,

(Franks and Williams 1985, Morton 1985). The inequality is sharp for all Prime Knots up to 10 crossings with the exceptions of 09-042, 09-049, 10-132, 10-150, and 10-156.

**References**

Franks, J. and Williams, R. F. ``Braids and the Jones Polynomial.'' *Trans. Amer. Math. Soc.* **303**, 97-108, 1987.

© 1996-9

1999-05-26