  Every knot has a plat projection, obtained by closing up a braid with
bridges. The plat projection is determined by the number of strands and the
number of rows of twist regions in the braid, and an integer number of
crossings in each twist region. In recent work, we showed that under certain
restrictions, including that the number of rows is odd, a minimal width plat
projection is unique. In this paper we extend the results to even plats. Using
new arguments, we show that if each of their twist regions contains at least
three crossings, and their length is sufficiently long with respect to their
width, then the projection is unique. This essentially "doubles" the set of
knots for which such diagrams classify the links.

Geometric Topology