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|Kimberling Shuffle KIMBERLING SEQUENCE King Walk DELANNOY NUMBER |
Kinoshita-Terasaka Knot This sequence has GENERATING ... Kinoshita-
Terasaka Mutants Kinoshita-Terasaka Mutants References Adams, C. C. The
|FIGURE 4.9 Kinoshita–Terasaka mutants. tangles T1 and T2 given by the |
sequences of integers i , j , k, ... ,l,m and n, p, q, ... ,r,s. The two rational tangles T1
and T2 are equivalent if and only if the corresponding continued fractions m + 1/[ l
|1 1 1]) and were used by Morton and Traczyk and independently by J. Murakami |
to distinguish, inter alia, the Kinoshita-Terasaka and Conway knots (figure 1 1),
the most famous example of mutants. Again, there is no sense in trying to ...
|Mutants are big trouble in general. As we saw in Section 5.3, they cannot be |
distinguished by hyperbolic volume either. We did see that the Kinoshita-
Terasaka mutants were distinguishable because their minimal genus Seifert
surfaces had ...
|Namely, the Seifert matrices of any knot and its Conway mutant are S-equivalent, |
so that their Alexander polynomials and ... Example 3.8.4- The Conway knot KC
shown in 3.8.1b is an elementary Conway mutant of the Kinoshita-Terasaka knot
|MUTANTS. OF. KNOTS. JOZEF H. PRZYTYCKI 0. Introduction. There is the nice |
formula which links the Alexander polynomial of (m, )t)-cable of ... On the other
hand they were unable to distinguish the Conway knot and the Kinoshita-
|Mutants and tangles A tangle is a portion of a link diagram from which there |
emerge just 4 arcs pointing in the compass directions AW, NE, SW, SE, ...
Famous mutants: the Conway and Kinoshita-Terasaka 5.3 The Homfly
|D Application Let M be a hyperbolic 3-manifold, By a mutation of M we mean |
cutting M along an embedded ... For discussion of mutation invariants, see
Further Reading. ... Figure 5.9 shows the Kinoshita-Terasaka and Conway
|This operation is called mutation and the two knots are said to be mutants. In Fig. |
9, we have indicated the three mutation operation 71,- 's. An example for the
mutant knots is the well-known eleven-crossing Kinoshita-Terasaka and Conway
|1 Mutants have long been known to have the same Alexander polynomial, and |
more recently to have the same polynomial P , Possibly the best known mutant
pair are the inequivalent knots of Conway and Kinoshita-Terasaka which both ...