COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

348 J. H. Conway
3 and 4 string links to 9 crossings
Link
Z&2
.1
2,2,2-
2,2,2+
4,222
31,2,2
2,2,2+ +
c&2> (2, 2)
.3
.2:20
4,2,2-
3 1,2,2-
@,a c&2-)
c&2) - c&2)
29% 2, 2
2,2,2,2-
2,2,2,2--
2 1 2,2, 2
21 11,2,2
3,2,2,2
21,2,2,2
4,2,2+
3 1,2,2+
2,2,2+++
(2,2+)(2,2)
(292) 1 C&2)
.211
.21:2
. c&2)
212,2,2-
21 11,2,2-
3,2,2, 2-
2 1,2,2,2-
3,2,2,2- -
(2,2+j (2,2-j
(2,21-I-(2, 2)
.a 2-I
. - c&2)
2,2, 2, 2+
+1+1+1
W> - id M{4
0 0 0
+1+1-1
(4 is) 01
- {r-?sf}
+1+1-1
{r> Id it)- {r-14
+2+1-t-1
i2+1+1
VWr4 - PI {sl it>) - (4
kW4 - G-1 1.4 01) - 01
+1+1+1
+2+2 0
Tl 0 0
Ofl-1
+2+1-1
WF2{rl{sl ItI
W W V’t> + 6-1 @I (4
W if-> 49 PI
- it> - G-> Is> (4 {r4
-{r-W?}
+2+1-1
{f}- {rs} {r-‘sf}
f2 0
+2+2
+l+l
0
0
0 0+1+-l
- w (4 14
W (4 (4 + 13 {rd W
{rsfu-rs-lt-lu}-{r}{s}{t}{u}
+ 1-F 1 0 Of 1 - 1 (rt-‘} {su-~}- {rs-‘} {rzf}
+1+1 0 0+1+1 {mu-rs-‘t-‘u}
o-i-1-1
09 WWlO+ b-> 14 ON - (4
0+1-1 - {r> {4(W’O + {r> Is> it>) - (0
+1+1-1
(1 - {r*}){r-‘sf)+ {r} {s} {t} {r*}
+1+1+1
+2+1-1
W4 - (4 W - HW 01
(r} {s} {f} {r%}- {r-W>
i-2+1-1
flfl-1
W({rl{s> {tl - {r-W) + (4
2(r) {s} {t}- {r-lst}
0+2 0
0 0 0
t-1 0 0
-I-2+1-1
- (4 1s) 14 - W2{4 {rW
14 61 W + WW {G
w~~~*~4
-{r}z{s}z{t)-{r~zs~t}
0 0 0
0+1+1
- WY4 if>
09 Is> W?+ W
0+1+1 (f) - {r} {s} {rsf -‘}
+1+1+1 {r*~(W - b-1 (4 +I) - btj
+1+1-1 {r} {Psf}- {rsf} - {r} {s} {f}
+1+1-1 - {r} (s-‘f}- {r-%f}
0 0 0 W {d (4
0+2 0 - b-1 (4 {r*4
f2 0 0 0 {r}z{f} (r-5)
0 0 0
+ 1 + 1 0 0+ 1 - 1 (rf-‘} {.su-~} --{Kv-~} {fu}+
WW PI h>
Enumeration of knots and links
10 crossing alternating knots. Basic polyhedron l*
T knot s 60 A
120 82 r 17/8 [9-4
119 712 r 2318 [-3+3-3+3-l
102 64 r 2516 [13-6
122 613 r 2717 [-7+7-3
117 61 12 r 33/13 [5-5+5-3+1
81 532 r 37/16 [7-7+6-2
78 5212 r 43/16 [-15+11-3
121 514 r 2916 [5-5+5-2
101 5 113 r 39/11 [-7+7-5+3-l
108 51112 r 45117 [17-11+3
80 433 r 43/13 [-13+11-4
24 4312 r 47/17 [-ll+lO-6+2
74 4222 r 53/22 [23-13+2
68 42112 r 57/22 [13-12+8-2
106 4132 r 43119 r-9+9-6+2
79 4123 r 47114 I-15+12-4
37 4114 f 4119 [9-7+5-3+1
67 41122 r 55/23 r-19+14-4
107 41113 r 51/14 [-ll+ll-7+2
77 352 r 35/16 [-11+9-3
66 3412 r 45/16 [9-9+7-2
76 3313 r 49/13 [13-10+6-2
20 33112 r 59/23 [-15+13-7+2
65 3232 r 55124 [-19+14-4
61 32212 r 65/24 [17-14+8-2
71 32113 r 61/17 [17-13+7-2
16 321112 r 71/27 [-19+16-8+2
105 3 13 12 r 53/19 [19-13+4
62 31222 r 63/26 [-17+15-7+1
60 312112 r 67126 r-25+17-4
21 31132 r 57/25 [21-14+4
58 311122 r 69/29 [19-15+8-2
22 311113 f 65/18 [25-16+4
104 2512 r 37/13 [13-9+3
52 2422 r 49/20 [21-12+2
51 24112 r 51/20 r-19+13-3
15 2332 f 53/23 [19-13+4
49 23122 r 59/25 [-21+15-4
48 22312 r 61/22 [15-13+8-2
11 222112 r 75/29 r-21+17-8+2
41 221212 r 71/26 r-21+17-7+1
3 2211112 r 81/31 [27-19+7-l
14 212212 f 73127 [23-17+7-l
43 2121112 r 79/30 r-25+19-7+1
1 21111112 f 89/34 [31-21+7-l
349