Stevedore knot (mathematics)
|Common name||Stevedore knot|
|Dowker notation||4, 8, 12, 10, 2, 6|
|Last /Next||52 / 62|
|alternating, hyperbolic, pretzel, prime, slice, reversible, twist|
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the (5,−1,−1) pretzel knot.
The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop.
its Conway polynomial is
and its Jones polynomial is
The Alexander polynomial and Conway polynomial are the same as those for the knot 946, but the Jones polynomials for these two knots are different. Because the Alexander polynomial is not monic, the stevedore knot is not fibered.