The minimal-crossing conjecture for highly twisted plat diagrams

Consider a knot or link diagram satisfying the conditions of Theorem~; in particular, the diagram is a sufficiently long plat with at least three crossings in each twist region. Minimal-crossing conjecture. Knot and link diagrams satisfying the conditions of Theorem~ realize the crossing number of the associated links. If true, these canonical highly twisted plat projections would have minimal crossing number, supporting enumeration by crossing number as well as by bridge number; the source presents this as an open conjecture.