Morton-Franks-Williams Inequality
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 10crossings with the exceptions of 09-042, 09-049, 10-132, 10-150, and10-156.See also Braid Index
References
Franks, J. and Williams, R. F. ``Braids and the Jones Polynomial.'' Trans. Amer. Math. Soc. 303, 97-108, 1987.
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