COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

356 J. H. Conway
Alternating 11 crossing knots. Basic polyhedron not 1*
L knot L knot L knot L knot
75 .41.2 7 .3.20.2.20 53 20.3.2.2 155 9*2.2
229 .41.20 43 .21.20.2.20 176 2.3.20.20 44 9*2.20
264 .3 11.2 50 .(3, 2).2 196 2.2 1.2 0.2 0 149 9*2 0.2
98 .3 11.20 200 .(2 1, 2).2 8 2 0.3.2 0.2 39 9*2: 2
263 .2 3.2 51 .2.(3, 2) 64 20.2 1.20.2 161 9*2:20
97 .23. 20 195 .2.(2 1, 2) 167 2.2.2.2.2 0 168 9*2 0: .2 0
288 .2 12.2 178 .(3, 2).2 0 157 2.2.2.2 0.2 0 145 9*.2: .2
110 .2 1 2.2 0 204 .(2 1, 2).2 0 169 2.2 0.2.2.20 153 9*.2: .20
305 .2 1 1 1.2 177 .2 0.(3, 2) 212 8*2 2 147 9’ : 2 0.2 0
303 .2 1 1 1.20 197 .20.(2 1,2) 191 8*2 1 1 163 9*20: : 20
74 .4.2 1 73 22:2:2 61 8*4 0 148 10*2 0
76 .4.2 10 65 211:2:2 214 8*3 1 0 150 10**2
265 .3 1.2 1 59 4:2:20 188 8*2 1 1 0 410 10**2 0
267 .3 1.2 10 226 3 1:2:20 4 8 8*3.20 151 10** :2
285 .2 2.2 1 262 2 1 1 : 2 : 2 0 190 8*2 1.2 0 144 100**:20
286 .22. 210 170 40:2:2 173 8*3 0.2 0 411 11*
58 .4.2.2 71 310:2:2 198 8*2 1 : 2
219 .3 1.2.2 209 2110:2:2 172 8*3: 2 0
256 .2 1 1.2.2 206 22:20:20 192 8’2 1 0 : 2
244 .2 2.2.2 0 205 21 1:20:20 47 8*30:20
261 .2l 1.2.20 242 220:2:20 199 8*2 1 0 : 2 0
11 .4.2 0. 2 257 2 1 1 0 : 2 : 2 0 193 8*2 1 : .2
228 .3 1.2 0.2 9 40:20:20 4 9 8”3: .20
95 .211.20.2 227 310:20:20 201 8*210:.2
243 .2 2 0.2.2 63 2 1 1 0 : 2 0 : 20 174 8*3 0: .2 0
260 .2 1 10.2.2 69 3:21:2 189 8*2 1’0: .2 0
186 .2.4.2 217 3: 2 1 : 2 0 171 8*3 : : 2 0
54 .2.3 1.2 237 2 1: 2 1 : 2 0 146 8*2 1 : : 2 0
213 .2.2 2.2 86 3:210:2 46 8*3 0 : : 2 0
10 .2.4 0.2 259 21:210:2 403 8*2.2 0.2
184 .2.3 10.2 223 30:21:2 154 8*2.2 0.2 0
72 .2.2 2 0.2 221 3:210:20 1 6 6 8*2.20:2
66 .3.2 1.2 87 30:21:20 4 0 8*2.20:20
224 .3.2 1.2 0 216 30:21 0:2 404 8*2 0.2 : 2
255 .2 1.2 1.20 67 30:21 0:20 405 8*20.2:20
70 .3.2 10.2 214 2 1 0: 2 1 0 : 20 156 8*2 0.2 0 : 2 0
215 .3 0.2 1.2 194 2 1.2.2.2 164 8*2 0.2 : .2
258 .2 1 0.2 1.2 56 3.2.2.2 0 41 8* 20.2 : .2 0
218 .3.2.2 1 181 3.2.2 0.2 158 8*2 0.2 0: .2
236 .2 1.2.2 1 55 3.2 0.2.2 165 8’2 : 2 : 2 0
222 .3.2.2 10 202 2 10.2.2.2 162 8*2 : 2 0 : 2 0
68 .3.2 0.2 1 180 3 0.2.2.2 0 62 8*2 0 : 2 0 : 2 0
239 .2 1.2 0.2 1 207 210.2.2.20 42 8*2: .20: .2
88 .3 0.2.2 1 6 3 0.2.2 0.2 152 8*2: .2: .20
175 .3.2.2.2 45 2 10.2.2 0.2 57 9*3
159 .2 1.2.2.2 179 3 0.2 0.2.2 406 9*2 1
211 .2 1.2.2.20 160 2 10.20.2.2 185 9*30
182 .3.2.2 0.2 203 2.2 1.2.2 407 9*.3
52 .3 0.2.2.2 183 2.3.2.2 0 408 9*.2 1
210 .2 1.2.20.20 208 2.2 1.20.2 409 9*.3 0
Non-alternating 11 crossing knots
4 2, 3,2-
42,212-
41 1,3,2-
41 1,21,2-
3 1 2, 3,2-
312,21,2-
3111,3,2-
3111,21,2-
24,3,2-
24,21,2-
2 3 1, 3,2-
23 1,21,2-
2 1 3, 3, 2-
21 3,21,2-
2121,3,2-
2121,21,2-
21 12,3,2-
2112,21,2-
21 11 1,3,2-
21111,21,2-
5,22,2-
5,2 1 1,2-
4 1,2 2,2-
41,21 1,2-
32,22,2-
32,211,2-
3 11,22,2-
311,211,2-
2 3, 2 2,2-
23,211,2-
221,22,2-
221,211,2-
5, 3, 2 l-
4 1, 3, 3-
41,21,21-
3 2, 3, 2 l-
3 1 1, 3, 3-
311,21,21-
2 3, 3, 3-
2 3,21,21-
221,3,21-
2 12, 3, 3-
212,3,21-
212,21,21-
2 111,3,3-
21 11,3,21-
21 11,21,21-
Enumeration of knots and links
4,22,3-
4,2 2,2 l-
4,2l 1,3-
4,21 1,21-
3 1, 2 2, 3-
3 1,22,21-
31,211,3-
31,21 1,21-
22,22,21-
22,21 1,3-
211,211,21-
3, 3, 3, 2-
3,3,2 1,2-
3,2 1, 3,2-
3,2 1,2 1,2-
2 1,3,2 1,2-
2 1,2 1,2 1,2-
3, 3, 3, 2- -
3, 3,2 1, 2- -
3,2 1,3,2- -
(2 2, 2) (3,2-l
(2 2, 2) (2 1,2-l
(2 1 1, 2) (3,2-)
(2 1 1,2) (2 1,2-l
(3, 2 1) (3,2-)
(3,2 1) (2 1,2-)
(3,2+) (3,2-)
(3,2+) (2 1,2-)
(2 1,2+j (3,2-)
(2 1,2+) (2 1,2-l
(2 2,2-l (3,2)
(22,2-)(21,2)
(21 1,2-)(3,2)
(21 1,2-)(21,2)
(3, 3-) (392)
(3, 3-) (2 192)
(2 1,2 l-) (392)
(21,21-)(21,2)
(2 2, a- (332)
(22,2)-(21,2)
(21 l,2)-(332)
(2 1 1,2)-(2 l,2)
(3,2 l)-(332)
(3, 2 w-(2 122)
(3,2+)-(3,2)
(3,2+)-(2 192)
(2 I, 2+)-(3,2)
(2 1,2+)-(2 1,2)
357
: :
.(3,2-).2
2.-21.2.2
.(2 1,2-).2 2.21.-2.2
.2.(3,2-)
2.-3.2.20
.2.(2 1,2-) 2.3.-2.20
.(3,2-).20 20.3.-2.2
.(2 1,2-).2 0 2.-3.-20.20
.2 0.(3,2-) 2.-21.-20.20
.2 0.(2 1,2-) 20. -3. -20.2
. -(3,2).2 20.-21.-20.2
. -(2 1,2).2 2.2.-2.2.20
.2. -(3,2)
2.2. -2.20.20
.2. -(2 1,2) 2.20.-2.2.20
.(3,2).2 0 8*-40
.20.-(3,2)
8*-310
-22:2:2 8*-21 10
-220:2:20 8*-3 0.20
-22:20:20
8*3 : -20
-22: -20: -20 8*-210:2
22: -20: -20 8*-30:20
-211:2:2
8*30: -20
-2110:2:20 8*-210:20
-211:20:20
8*-210: .20
-211:-20:-20 8*-30:.20
-40~2~2
8*-210: .20
-4~2~20
8*30:: -20
-40:20:20 8*3: : -20
-40: -20: -20 8*2 1 :: -20
-310:2:2
8*2. -20.2
-310:20:20 8*2.-20.20
-3 1 o:-20: -20 8*2.20.-20
-2110:2:2 8*2:2: -20
-211:2:20 8*2:20:-20
-2110:20:20
8*2 - 2 0 20
-21 10: - 20: -208*20: -20:20
-30:21:2 8*20:20: -20
-30:21: -20 8*2 : .-20: .2
-30:210:2 8*2: .2: .-20
-210:30:2 9*.-3
-210: - 30: -20 9*.-21
-210:21:2 9*2. -2
-210:-2lO:-209*20.-2
9*.2: .-2
9*.-2: .-2
9*.20: .-2
10*-2 0
10**-2 0