COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

344 J. H. Conway
2 string links to 8 crossings
Link A s uo units 60 A
0
2
4
212
6
33
222
412
3112
232
3,232
21,2,2
.2
3,2,2-
2 1,2,2-
8
53
422
323
3122
242
21212
211112
2 2,2,2
211,2,2
3,2,2+
2 1,2,2+
.21
.2:2
2 2,2,2-
2 11,2,2-
0 4, r, s, t
+ 11 qr, w, t
f2 rs, t
0 r, s, t
+3 rs, t
+3 qr,qs,t
+2 rs, t
+ 1 rs, t
-t 1 rs, t
0 r, s, t
0 r,s
+2 rs
0 r,s
i2 rs
0 r,s
+4 rs, t
+4 rs,t
13 rs,t
+4 rs,t
+3 rs, t
i2 rs, t
+l rs, t
+1 r, 3, t
i-1 rs
0 r,s
$2 rs
0 r,s
0 r,s
+2 rs
0 r, s
+2 rs
0 + O/l 0
0 + 2/l 1
+1 +
+1 + ii: ITS) -{rl is)
i-2 73 6/l {r2sZ}+1
0
+1
+5
T3
10/3 {rZ+s2}- 1
W5 {rsl+{rl {s>
+2 zp7
14/5 I-{r}{s}{rs)
I1 0 + +3 1617 18/7
~---r{ls~{r-'sl
-3 -I- 16 {r}GlL?
+1 - 5 20 {r-3s}+2{r}3{s}
+l +3 24 {rl {sl+{r13 (31
-3 -t
4 {t-3>
+1 + 88 -{r> Is>
+3 + 8/l {r3s3+rs}
-1 + 16/5 {r}{s}+{rs}{rZs-f}
+2 +11 2219 {2r2s2-r2-s2}+3
+1 T3 24/7 {rs}{rz+s2-1)
0 +13 26/11 {2r2+2s*+r2-s2}-3
+1 +5 20/9 {rs}+2{r}{s}
-i-2 +3+5 30/11 1-(r)2{s}2
1-2 +17 34/13 l+{r}2{s}2
- 1 +7 28 {4r-‘s-2rs-re3s}
-1 + 32 -{r13{sl
-3 i7 28
~;~~;2{rl{sl {r2)
+1 + 32
+1 - 5 40 {r~3{sHr~{s~
- 1 - 3 36 {@SF 4(r) {sl
-1 + 88 {r> {s>
-1 f3 12 {2r-‘s-re3s}
9 crossing knots
A&B T/L knot
9, 41
9* 38
9, 40
9, 39
9, 33
9, 37
9, 34
9 12 31
9 11 30
9 14 28
9, 26
9 lo 32
9 13 25
9 13 39
9 20 21
921 18
9 26 17
9, 16
9 15 15
9 19 14
9 23 12
9 17 22
9 27 8
9 2
31
9 36 24
9 45 13
9 22 23
9 4
9;; 36
9 37 19
9 16 27
92, 20
9 28 6
9 33 3
9 32 7
9 38 5
9 29 11
9 39 9
9 PI 10
9 34 1
9 40 35
9 42 IV
9 44 I
9 43 v
9 45 111
9 46 VI
9 48 VII
9 II
9 4, VIII
9 49
Enumeration of knots and links
s f.70 A
99 r 9/l
72 r 1517
63 r 1916
54 r 2115
522 r 2715
513 r 2316
423 r 3119
4212 r 35113
4122 r 33114
41112 r 37114
342 r 29113
333 r 33110
3222 r 41117
3213 r 37110
31212 r 41115
31122 r 43118
311112 r 47118
2412 r 31111
2322 r 39116
23112 r 41116
22122 r 45119
21312 r 39114
212112 r 49119
2111112 r 55121
2 2, 3, 2 r 37
22,21,2 r 47
21113,2 r 43
211,21,2 r 53
3,373 r 27
3,21,2 1 r 45
3,3,2-c r 39
3,2 1,2+ r 45
2 1, 2 1,2+ r 51
.21.2 n 61
.21.20 n 59
.2.2.2 r 57
.2.20.2 r 51
2:2:20 r 55
20:20:20 r 49
8'20 r 69
9* r 75
2 2, 3,2- r 7
2 2,2 1,2- r 17
21 1,3,2- r 13
211,21,2- r 23
3, 3, 2 l- r 9
21,21,21- r 27
-2O:-20:-20 r 25
8*-20 r 27
[l-1+1-1+1
I-7+4
r-3+3-3+2
[5-5+3
r-5+5-4+2
[-11+6
[-7+6-4+2
[-13+9-2
[7-7+5-l
[15-9+2
[9-7+3
[9-8+4
[13-10+4
[ll-9+4
[11-9+5-l
[--17+11-2
[-13ill-5+1
[- 11+8-2
I-15+10-2
[17- 10+2
[15-11+4
r-9+9-5+1
[15-11+5-l
r--17+13-5+1
[9-8+5-l
f-17+12-3
L-11+10-5+1
[17-12+5-l
[- 13+7
[19-llf2
i-9+8-5+2
[13-10+5-l
[-15+12-5+1
119-14+6-l
i- 17+14-6+1
r19- 14+5
i-15+12-5+1
r-21+14-3
[19- 12+3
[23-16+6-l
I-23+18-7+1
[-1+2-l
[7-4+1
[1-2+3-l
[-9+6-l
[5-2
[-11+7-l
[7-6+3
L-5+6-4+1
345