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8Kb

ORDERING KNOTS

Slavik V. Jablan

 

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.

 

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