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.

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

**Colorization Invariant **__2-2-2-1__

__Class 1__ does not split.

__Class 2__

**49** ... 7-10 ... **DISTINCT**
**1** ... 8-17, 9-14, 9-58

__Class 3__ does not split.

__Class 4__

**63** ... 9-60 ... **DISTINCT**
**15** ... 9-26 ... **DISTINCT**

__Class 5__
**49** ... 9-29 ... **DISTINCT**
**1** ... 9-44 ... **DISTINCT**

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

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

**Colorization Invariant **__3-2-2__

The only class affected is

__Class 2__

**25** ... 8-17 ... **DISTINCT**
**1** ... 9-14, 9-58

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

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

**Colorization Invariant **__4-2-1__

The only class affected is

__Class 3__

**33** ... 9-58 ... **DISTINCT**
**17** ... 9-14 ... **DISTINCT**

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

- 3-1, 9-66
- 9-1, 9-25

**Colorization Invariant **__6-1__

__Class 1__ does not split.

__Class 2__

**10** ... 9-1 ... **DISTINCT**
**4** ... 9-25 ... **DISTINCT**

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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