This is the simplest 3-page diagram of knot 3_1 (the trefoil knot).
This is the simplest non-trivial knot. Its simplest planar diagram has 3 crossings. A list of other knots with small crossing number can be found in  and . 3_1 is an alternating knot. It is chiral and invertible. It is also the torus knot of type (2,3). Here we give the simplest 3-page diagram of the trefoil knot. It has 8 vertices. 3-page diagrams were introduced in . According to the notation given in  this diagram is encoded by the word a_1a_0a_0d_2d_1c_0c_0c_2.
|Keywords||knot; link; 3-page representation|
Submitted: Sun Sep 10 07:10:24 CET 2000.
Accepted: Mon Nov 20 17:06:57 CET 2000.
Moscow State University
Department of Mechanics and Mathematics