Geodesic
Ordering Knots
Using geometric-combinatorial methods, the complete list of prime alternating links with n £ 12 crossings, is derived. All the liks obtained, belonging to the corresponding subworlds and given in Conway notation, are classified in infinite series of links - the families. Combinatorial formula giving the number of rational links for every n is derived, as well as some combinatorial results for the number of polyhedral source links for n £ 12. The generating links for n £ 9 are represented by their projections, i.e. by bicolored graphs. Amphicheirality is recognized from the antisymmetry of vertex-bicolored link projections.
Classification : 57M25 
@article{VM_1999_1_1_a6,
     author = {Slavik V. Jablan},
     title = {Ordering {Knots}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_1999_1_1_a6/}
}
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Slavik V. Jablan. Ordering Knots. Visual Mathematics, Tome 1 (1999) no. 1. http://geodesic.mathdoc.fr/item/VM_1999_1_1_a6/