  It has been conjectured that the algebraic crossing number of a link is
uniquely determined in minimal braid representation. This conjecture is true
for many classes of knots and links.
  The Morton-Franks-Williams inequality gives a lower bound for braid index.
And sharpness of the inequality on a knot type implies the truth of the
conjecture for the knot type.
  We prove that there are infinitely many examples of knots and links for which
the inequality is not sharp but the conjecture is still true. We also show that
if the conjecture is true for K and L, then it is also true for the (p,q)-cable
of K and for the connect sum of K and L.
