Distinguishing Links - Part VI

APPLYING COLORIZATION INVARIANTS - Permutation Group S(7)

Up to this point, 106 out of the original 118 links have been shown distinct. The remaining 12 belong to the following 5 classes.

  1. 3-1, 9-66
  2. 7-10, 8-17, 9-14, 9-58
  3. 9-1, 9-25
  4. 9-26, 9-60
  5. 9-29, 9-44


Colorization Invariant 2-2-2-1

Class 1 does not split.

Class 2

Class 3 does not split.

Class 4

Class 5

At this point, 111 out of the original 118 links have been shown distinct. The remaining 7 links belong to the following three classes.

  1. 3-1, 9-66
  2. 8-17, 9-14, 9-58
  3. 9-1, 9-25


Colorization Invariant 3-2-2

The only class affected is

Class 2

At this point, 112 links have been shown distinct, and the remaining 6 links form the following 3 classes.

  1. 3-1, 9-66
  2. 9-1, 9-25
  3. 9-14, 9-58


Colorization Invariant 4-2-1

The only class affected is

Class 3

At this point, 114 links have been shown distinct, and the remaining 4 links form the following two classes.

  1. 3-1, 9-66
  2. 9-1, 9-25


Colorization Invariant 6-1

Class 1 does not split.

Class 2

Therefore, once the 7-permutation invariants have been applied, 116 links have been shown distinct, and the only remaining links are 3-1 and 9-66. These will be shown distinct in this page.


Charilaos Aneziris

Copyright 2002

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