COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

352
Non-alternating
J. H. Conway
L knot Is 60 A 10 crossing 2 string links
61 5, 3,2- r 1 [--l+l+O-l+l
11 5,2 1,2- r 11 r-1+2-2+1
31 4 1,3,2- r 19 I-5+4-2+1
41 4 1,2 1,2- r 29 [7-6+4-l
61V 32,3,2- r 11 [l+l-3+2
111 3 2,2 1, 2- r 25 [9-6+2
31V 31 1,3,2- r 17 [5-4+2
411 311,21,2- r 31 [-11+8-2
3v 2 3, 3, 2- r 5 [l-1+1
4111 2 3,2 1,2- r 19 [-7+5-l
6V 221,3,2- r 23 r-3+4-4+2
1IV 221,21,2- r 37 [13-9+3
2v 2 2,2 2, 2- r 15 [-5+4-l
21V 22,21 1,2- r 25 [11-6fl
2VI 21 1,211,2- r 35 r-7+8-5+1
6111 4,3,3- r 3 [-3+2+0-1+1
311 4, 3,2 l- r 9 [3-2+1
21 4,2 1, 2 l- r 21 [5-4+3-l
611 3 1. 3, 3- r 15 [-1+2-3+2
3111 3 1, 3,2 l- r 27 i-7+6-3+1
2111 31,21,21- r 39 r-13+10-3
51 22,3,3- r 3 r-3+1+1
1111 22,21,21- r 33 [13-8+2
211 21 1,3,21- n 27 [-9+7-2
3vII (3,2) (3,2-j n 31 r-9+7-3+1
4VIII (392) (2 1,2--j n 41 [11-9+5-l
4VI (2 I,21 (3,2-j n 29 [7-6+4-l
31X (2 1,2) (2 1,2-l n 43 [--13+10-4+1
6VIII (3,2)- (3,2) r 11 [-5+4-l-1+1
1VI (3,2)-(2 1,2) n 1 [3-l--1+1
6VII (2 1,21-e 1,2) r 17 [7-4fO+l
2vII -3:2:2 r 25 [7-5+3-l
3x -3:2:20 r 35 r-9+8-4+1
4VII -3:20:20 r 49 [13-11+6-l
2VIII -30:2:2 r 45 [15-10+4-l
3VIII -30:2:20 r 49 r-11+9-4+1
4v -30:20:20 r 21 [3-4+4-l
511 3: -20: - 20 r 5 [3-2+0+1
6VI 21: -20: -20 r 5 [3-2+0+1
21x -30: -20: -20 r 35 r-11+9-3
3VI 8*-3 0 r 51 r-15+12-5+1
1v 8’2: -20 r 45 [17-llf3
41V 8*2: .-20 r 39 r-15+10-2
10 3, 3, 2, 2
73
622
3, 2 1, 2, 2
2 1, 2 1, 2, 2
55 3, 2, 3, 2
523
3, 2, 2 1, 2
5122 2 1, 2, 2 1, 2
442 5, 2, 2f
424 4 1, 2, 21
4213
3 2, 2, 2-v
41212 3 1 1, 2, 2+
411112 2 3, 2, 2+
343
2 2 1, 2, 2+
3322 4, 3, 2-t
3223 4, 2 1, 2+
32122 3 1, 3, 2+
3142 3 1, 2 1, 2+
31213 3, 3, 3+
311212 3, 2 1, 2 1+
3111112 22,2,2+-b
262
2 1 1, 2, 2f
23212 3, 2, 2+ + +
231112 21,2,2+++
22222 (2 2, 2) (2, 2)
221122 (2 1 1, 2) (2, 2)
21412 (3, 2 1) (2, 2)
213112 (3, 2+) (2, 2)
2112112 (21,2+)(2,2)
4 2, 2, 2 (3, 2) (2, 2+)
41 1,2,2 (2 1, 2) (2, 2+)
3 1 2, 2, 2 (3, 2) 1 (2, 2)
31 11,2,2 (2 1, 2) 1 (2, 2)
2 4, 2, 2 .4 1
231,2,2
.3 1 1
2 1 3, 2, 2 .2 3
2 1 2 1, 2, 2 .2 1 2
2 1 1 2, 2, 2 .2111
21111,2,2 .2 1 1.2
4, 2 2, 2
.2 11.20
4,21 1,2 .3.2 1
31,22,2 .3.2 10
3 1, 2 1 1, 2 .4:2
2 1 2, 3, 2 .31:2
2 1 2, 2 1, 2 .211:2
21 11,3,2 .22:20
2 111,2 1,2 .21 1:20
2 2, 3, 3 .3:21
22,21,21 .3:210
2 1 1, 3, 2 1 .21:21
Enumeration of knots and links
.2 1.2.2
.2 1.2 0.2
.2.3.2
.2.3 0.2
.2.2 1.2 0
.2.2.2.2
.2.2 0.2.2 0
.(3, 2)
.(2 1, 2)
.(2, 21.2
.(2, 2j.20
21:2:20
210:2:2
210:20:20
2.2.2 0.2 0
2.2 0.2.2 0
2 0.2.2.2 0
8*2 1 0
8*2.2 0
8*2 0 : 2 0
8*2 0 : .2 0
8*2 : : 2 0
9*2
9*.2
10**
4 2, 2, 2-
4 1 1, 2, 2-
3 1 2, 2, 2-
3 111,2,2-
2 4, 2, 2-
2 3 1, 2, 2-
2 1 3, 2, 2-
2 12 1,2,2-
21 12,2,2-
2 1111,2,2-
4, 2 2, 2-
4, 2 1 1, 2-
3 1, 2 2, 2-
3 1,2 1 1,2-
2 1 2, 3, 2-
2 12,2 1,2-
2 11 1,3,2-
2 11 1,2 1,2-
2 2, 3, 21-
2 1 1, 3, 3-
211,21,21-
3, 3, 2, 2-
3, 2 1, 2, 2-
2 1, 2 1, 2, 2-
3, 2, 3, 2-
3, 2, 2 1, 2-
2 1, 2, 2 1, 2-
3, 3, 2, 2- -
3, 2 1, 2, 2- -
3, 2, 3, 2- -
3, 2, 2 1, 2- -
(2 2, 2) (2, 2-j
(2 1 1, 2) (2, 2-j
(2 2, 2-j (2, 2)
(2 1 1, 2-j (2, 2)
(3, 2 1) (2, 2-j
(3, 3-j (2, 2)
(2 1, 2 1-j (2, 2)
(3, 2f) (2, 2-l
(2 1, 2+) (2, 2-j
(2, 2+)(3, 2-j
(2, 2+) (2 1, 2-j
(2 2, 2) - (2, 2)
(2 1 1, 2)--G 2)
(3, 2 1) - (2, 2)
(3, 2+)-G, 2)
(21, 2+)-(2, 2)
(2, 2-t)-(3, 2)
(2, 2+)--Q 1, 2)
.(2,2-I.2
.(2, 2-).2 0
. -(2, 2j.2
.-(2, 2).2 0
-210:2:2
-210:20:20
-2lO:-20:-20
2. -2.-2 0.2 0
2. -2 0. -2.2 0
8*2.-20
8*20: -20
8*-20: -20
8*20: .-20
9*.-2
353