The general Alexander polynomials derived this way coincide with the general Alexander polynomials for the family p (p=2k+1) and subfamilies p 2, p 1 2 (p=2k+1) proved by A. Cavicchiolli, B. Ruini and F. Spaggiari. All the general formulas in new knot tables belong to the realm of experimental mathematics: they represent results that are estimated, extrapolated and conjectured. Hence, they need to be proved (or disproved).

As an example, we are giving the complete results, containing ordered Dowker codes and the Jones polynomials, for the knot family p, p=2k+1. The reader can find analogous complete tables for knots with n £ 7 crossings at the addresses:

http://www.mi.sanu.ac.rs/~jablans/knotab/

Knot family: 2k+1


Notation:

3        31
5        51
7        71
9        91

Dowker codes:

3        4 6 2
5        6 8 10 2 4
7        8 10 12 14 2 4 6
9        10 12 14 16 18 2 4 6 8
11        12 14 16 18 20 22 2 4 6 8 10
13        14 16 18 20 22 24 26 2 4 6 8 10 12
15        16 18 20 22 24 26 28 30 2 4 6 8 10 12 14
17        18 20 22 24 26 28 30 32 34 2 4 6 8 10 12 14 16
19        20 22 24 26 28 30 32 34 36 38 2 4 6 8 10 12 14 16 18

Alexander polynomials:

3        [1 -1
5        [1 -1 1
7        [1 -1 1 -1
9        [1 -1 1 -1 1
11        [1 -1 1 -1 1 -1
13        [1 -1 1 -1 1 -1 1
15        [1 -1 1 -1 1 -1 1 -1
17        [1 -1 1 -1 1 -1 1 -1 1
19        [1 -1 1 -1 1 -1 1 -1 1 -1

D(p) = 2k
å
i=0 
 		(-1)iti

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