COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

346 J. H. Conway
9 crossing 2 string alternating links, with basic polyhedron l*
link a V
612 +2
5112 f2
432 fl
414 0
4113 0
3312 +2
32112 +2
3132 +1
31113 0
252 0
22212 +1
221112 fl
5,292 0
41,2,2 +2
3 2,2,2 0
3 1 1, 2,2 -!-2
2 3,2,2 f2
2 2 1, 2,2 0
4, 332 f3
4,21,2 fl
3 1, 3,2 fl
3 1, 2 1, 2 +3
3,3, 2 1 f2
2 1,2 1,2 1 +3
2 2,2,2 + 0
21 1,2,2+ f2
3,2, 2+ + 0
2 1,2,2+ + f2
(3,2) (2,2) f2
(2 1, WC 2) f2
{r-Q}- {r} {s} {r2s2}
{rs}- {r} {s} {r-ls}t
1 - 2 if-> {4 04
-{r> is> ({r2+sZ)+ 1)
Cd {4 {r-‘d”
Ml -PI 14 {r-Is))
{rs} f {r} {s}(l - {r’ + s2})
1-2(r) {s} {r-Q}
y;y+s7- 1)
1 - 6 6 CG4 + O-1 14)
1+ 09 {Nrl {d - PSI)
b-1 (4 WI + 1)
{r-%)+2(r) {s} {r’}
G-1 {4 (W3 - 1)
{2r-% - r-4}+ 4(r) {s}
{2r% - r%}+ 3(r) {s}
2+9 @I W21 - 1)
{s2} - 1 + {r} {s) {r-?s} {s2}
I+ {r”s-3 + 2(r) {.s) {r-ls}
Cs”) - 1 + NW W @“I
{r2.G+1+{~}2({r2+~2}-l)
{r-?s}(l - {r} {s} {r-Q})
1 i {r2s2} + {rs} {r } {s} + {r}2{s}2
14 (4 (4 - {r2N
{2r-?s-r-3s}+{r}{s}((r2}-3)
C4 {4 Mr21 - 1)
{r-“d + ir> WC3 - {r’))
{F%+2{r} (s} (9)
{r-%} f {r>” ({r%} - {r) {s})
9 crossing 2 string links, otherwise
link a V
.4 0
.3 1 0
.22 0
.3.2 +1
.3.20 +1
.3:2 0
.3 :20 0
.21:20 +2
.2.2.20 +1
2:2:2 f3
2:20:20 0
8*2 +1
5,2,2- f2
4 1,2,2- 0
3 2, 2,2- t-2
3 1 1,2,2- 0
2 3,2,2- 0
221,2,2- +2
4, 3,2- +3
4, 2 1,2- +1
3 1, 3,2- +3
3 1,2 1,2- +1
3, 3,3- +4
3,21,21- -1
(322) (2,2-) 0
(2 1,2) C&2-) 0
(3,2-) (232) +2
(2 1,2-)P, 2) +2
(392) - (232) t-2
(2 1,2)-G 2) +2
2:-20:-20 +4
Enumeration of knots and links
{r} {s} ({r” - r2} + 1)
(3 WW2) - 3)
09 H3 - 4r2N
1 - {r) {W) @‘I - 1)
1+ {rl {s&> ({f? - 1)
209 14 WI - 1)
.- (4 {s 1 +-“W’> - 1)
{rd + W3M
({s2)- 1X1 + {r> (4 W)
1 +{r2s4} - 3(r) {s} {rs)
b-1 MC3 + {f-l {r~21)
1 -{f-l {sP{rsl
{r-5.s}
- G9 14 {r’l
{2r+s - r-Q}
-20-l (4
- G-1 is)
{rs}+2{r-3s-r-1s)
1 + {rm2s4}
l+{s}(r%}
1+{~4}+{r}{r~-2}
{~2Fl-{r~{4{r~~
{rm3s3+ rs}
“y;; y&l- 1
r s r
(4 (4 + WC4
64 - Iv31 bl
fj$- {r13W
{r} {r?} + {r?}
{A+ rse3}
341