Make your own free website on Tripod.com


6Kb

a) a flype; b) elementary flype and its vertex-coloring interpretation.


12Kb

Link projections with n £ 8 crossings.


13Kb

Link projections with n = 9 crossings.


10Kb

Link projections of polyhedral world.


2Kb

Nonequivalent projections of the link 222 and links derived from them.


4Kb

For example, for the amphicheiral knot 41 (22) we have:

d(41) = d(22) =





t
0
0
0
-1
-t
0
0
1
-1
t
0
0
1
-1
-t






= t4-2t2

In the same way, for all knot projections (n £ 7) given by their Dowker sequences:

31   3               4 6 2                          1 0  3
41   22             4 6 8 2                       1 0 -2  0
51   5               6 8 10 2 4                  1 0  5  0   5
52   32             4 8 10 2 6                  1 0  1  0   5
61   42             4 8 12 10 2 6             1 0 -4 -2  3  2
62   312           4 8 10 12 2 6             1 0  1 -1 -3  2
63   2112         4 8 10 2 12 6             1 0  2  0  3   0
71   7               8 10 12 14 2 4 6        1 0  7  0 14  0  7
72   52             4 10 14 12 2 8 6        1 0 -3  0 -2  0  7
73   43             6 10 12 14 2 4 8       -1 0 -1  0  8  0  7
74   313           6 10 12 14 4 2 8        1 0 -4  0  2  0  7
75   322           4 10 14 12 2 6 8       -1 0 -2  1  4  0  7
75'   322'          4 10 12 14 2 8 6       -1 0 -3  0  4  0  7
76   2212         4 8 12 2 14 6 10         1 0 -1 -1 -1 -2 3
76'   2212'        4 8 12 10 2 14 6       -1 0  0 -1  3 -1  3
77   21112       4 8 10 12 2 14 6         1 0 -1 -1 -1 -2 3
77'   21112'     4 8 12 10 2 14 6        -1 0   0 -1  3 -1 3


Among them, to the amphicheiral projections of 41 (22) and 63 (2122) correspond even polynomials [46].

Liang polynomial A(t) [28] is defined by the similar determinant, where aii = te, and aij = s if the vertices i, j are connected with the multiplicity s (s = 0,1,2). In this case, for the amphicheiral knot projections A(t) = A(t -1). For example, for the amphicheiral knot 41 (22) we have A(t) = A(t -1) = -4t2+8t-3+8t -1-4t -2.