UC Santa Barbara

Looking at the structure of minimal prime knot presentations, one can notice that there are often, perhaps always, segments that present either the trefoil or the figure-eight knot. This note explores the question as to whether this is always the case, reporting on conversations with Jablan Slavik that began at a [Formula: see text] conference in Trieste, Italy and which never reached a conclusion. Evidence supporting this conjectured presence is reported and potential consequences are described.