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,
(Morton 1986, 1988, Franks and Williams 1987). 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.