Links with 2 components and 9 crossings

This table includes the knot designation, followed by the braid representation used by the braid programme, followed by the Alexander polynomial.

Output from braid v5.0.b1



-- L9(1)-a
s1-s2-s2s3-s2-s1s2-s4s3-s2s3s4-s3s2s3
Alexander polynomial = -3t^3+7t^2-7t+3

-- L9(1)-b
s1-s2s1-s2-s2-s2-s2-s2-s2
Alexander polynomial = -t^7+3t^6-3t^5+3t^4-3t^3+3t^2-3t+1

-- L9(2)-a
-s1s2-s1-s1s2s2s2s2s2
Alexander polynomial = -t^7+3t^6-5t^5+5t^4-5t^3+5t^2-3t+1

-- L9(2)-b
-s1-s2-s3s2-s3s4s3-s2s1-s3-s3s2-s3s2-s4
Alexander polynomial = -3t^3+11t^2-11t+3

-- L9(3)-a
s1-s2-s2s3s4-s3s2-s3-s2-s1s2-s4-s3s2s3
Alexander polynomial = -4t^3+11t^2-11t+4

-- L9(3)-b
-s1s2-s3-s3-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = 2t^5-6t^4+7t^3-7t^2+6t-2

-- L9(4)-a
s1s2-s3s2-s1s3-s2-s2-s2-s2s3-s2
Alexander polynomial = 2t^5-5t^4+5t^3-5t^2+5t-2

-- L9(4)-b
s1s2-s3s2-s1s3-s2s3-s2-s2-s2-s2
Alexander polynomial = 2t^5-5t^4+5t^3-5t^2+5t-2

-- L9(5)-a
-s1s2-s1-s1-s1s2s2s2s2
Alexander polynomial = t^7-3t^6+5t^5-7t^4+7t^3-5t^2+3t-1

-- L9(5)-b
-s1s2s3-s2s3s2-s4-s3s2s1-s2s3-s2-s3s4
Alexander polynomial = 4t^3-12t^2+12t-4

-- L9(6)-a
s1s2-s3s2-s1s3-s2-s2s3s3s3-s2
Alexander polynomial = 2t^5-6t^4+10t^3-10t^2+6t-2

-- L9(6)-b
-s1s2-s3s2s1-s2s3-s2-s3-s3-s3-s3
Alexander polynomial = 2t^5-7t^4+9t^3-9t^2+7t-2

-- L9(7)-a
s1s2-s3s2-s1s3s3s3-s2s3-s2-s2
Alexander polynomial = 2t^5-7t^4+13t^3-13t^2+7t-2

-- L9(7)-b
s1-s2s1-s2-s3-s3-s3s2-s3-s2
Alexander polynomial = 2t^5-8t^4+12t^3-12t^2+8t-2

-- L9(8)-a
-s1s2-s3-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = 2t^5-6t^4+9t^3-9t^2+6t-2

-- L9(8)-b
-s1s2-s3s4-s3-s2s1-s4-s4s3s2-s3-s3-s4s3-s2s3
Alexander polynomial = -4t^3+13t^2-13t+4

-- L9(9)-a
s1s2-s3s2-s1s3s3-s2s3-s2-s2-s2
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(9)-b
s1s2-s3s2-s1s3-s2-s2-s2s3-s2s3
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(10)-a
-s1-s2-s3s2-s3s4s3-s2s1-s3s2-s3-s3s2-s4
Alexander polynomial = -3t^3+9t^2-9t+3

-- L9(10)-b
-s1-s2-s3s2-s3s4s3-s2s1-s3s2-s3-s3s2-s4
Alexander polynomial = -3t^3+9t^2-9t+3

-- L9(11)-a
-s1s2-s3s2s1s2-s3s4-s3s2-s3-s3-s4
Alexander polynomial = t^5-7t^4+15t^3-15t^2+7t-1

-- L9(11)-b
s1-s2s1-s2-s3-s3s2-s3-s2-s2
Alexander polynomial = 2t^5-8t^4+13t^3-13t^2+8t-2

-- L9(12)-a
-s1s2-s1-s1s2s3s3-s2s3s2
Alexander polynomial = 2t^5-8t^4+15t^3-15t^2+8t-2

-- L9(12)-b
-s1s2-s3s4-s3s2s1-s3s2-s3s2-s4-s3
Alexander polynomial = t^5-7t^4+17t^3-17t^2+7t-1

-- L9(13)-a
s1s1s1s1s1-s2s1s1-s2
Alexander polynomial = t^7-3t^6+4t^5-4t^4+4t^3-4t^2+3t-1

-- L9(13)-b
-s1s2s2s2s2s2-s1s2s2
Alexander polynomial = t^7-3t^6+4t^5-4t^4+4t^3-4t^2+3t-1

-- L9(14)-a
s1s1-s2s1s1-s2-s2-s2-s2
Alexander polynomial = -t^7+3t^6-6t^5+8t^4-8t^3+6t^2-3t+1

-- L9(14)-b
s1-s2-s3-s3-s3-s3-s3-s2-s1-s2s3-s2
Alexander polynomial = -3t^5+7t^4-8t^3+8t^2-7t+3

-- L9(15)-a
-s1s2-s3s2s1s3s3-s2s3s3-s2s3
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(15)-b
s1s2-s3s2-s1s3s3s3-s2s3s3-s2
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(16)-a
-s1s2s2-s3s2s2s1-s2s3-s2-s3-s3
Alexander polynomial = 2t^5-7t^4+13t^3-13t^2+7t-2

-- L9(16)-b
s1-s2-s3s4-s3-s3-s2-s1-s2s3-s2-s4-s4
Alexander polynomial = 6t^3-16t^2+16t-6

-- L9(17)-a
-s1s2s2-s3-s3s2s2s1-s2s3-s2-s3
Alexander polynomial = 2t^5-6t^4+10t^3-10t^2+6t-2

-- L9(17)-b
-s1-s2-s2-s2-s3s4-s3s2s1-s2-s2-s3-s4-s3s2
Alexander polynomial = 5t^3-13t^2+13t-5

-- L9(18)-a
-s1s2s2-s3s2s1s3-s2s3s3-s2s3
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L9(18)-b
-s1s2s3s3-s2s3s2-s1s2s2
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L9(19)-a
-s1s2s2s2s2-s1s2s2s2
Alexander polynomial = t^7-3t^6+4t^5-5t^4+5t^3-4t^2+3t-1

-- L9(19)-b
-s1s2s2-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -2t^5+5t^4-6t^3+6t^2-5t+2

-- L9(20)-a
s1s1s1s1-s2s1s1-s2-s2
Alexander polynomial = -t^7+3t^6-6t^5+7t^4-7t^3+6t^2-3t+1

-- L9(20)-b
s1-s2s3s4-s3s2-s3-s2-s1-s2-s4-s3-s3-s3-s2
Alexander polynomial = 5t^3-12t^2+12t-5

-- L9(21)-a
s1s2-s3s2-s1s3s3-s2s3s3s3-s2
Alexander polynomial = -2t^5+7t^4-10t^3+10t^2-7t+2

-- L9(21)-b
s1s1s1-s2s1s1-s2-s2-s2
Alexander polynomial = t^7-3t^6+6t^5-9t^4+9t^3-6t^2+3t-1

-- L9(22)-a
-s1s2-s3s2s1s3-s2s3s3-s2-s2s3
Alexander polynomial = 2t^5-7t^4+14t^3-14t^2+7t-2

-- L9(22)-b
s1-s2-s3-s3-s3-s3-s2-s2-s1-s2s3-s2
Alexander polynomial = -3t^5+8t^4-12t^3+12t^2-8t+3

-- L9(23)-a
-s1-s1s2s2s2-s1s2s2s2
Alexander polynomial = -t^7+3t^6-6t^5+8t^4-8t^3+6t^2-3t+1

-- L9(23)-b
-s1-s2-s3-s3-s4s3s2s1s3-s4s3s2-s3s4-s3-s2-s4
Alexander polynomial = -4t^3+14t^2-14t+4

-- L9(24)-a
-s1-s2s3-s4s3s2s1s3-s4s3s2s3-s4s3-s2
Alexander polynomial = -t^5+7t^4-19t^3+19t^2-7t+1

-- L9(24)-b
s1-s2-s3-s3-s3-s2-s2-s1-s2-s2s3-s2
Alexander polynomial = -3t^5+9t^4-15t^3+15t^2-9t+3

-- L9(25)-a
-s1-s2s3-s4s3s2s1-s2s3s3-s2-s4s3
Alexander polynomial = -t^5+7t^4-16t^3+16t^2-7t+1

-- L9(25)-b
s1-s2s3-s4s3-s2-s1s3-s2s4s3s3-s2
Alexander polynomial = -t^5+7t^4-16t^3+16t^2-7t+1

-- L9(26)-a
-s1-s2s3-s4s3-s2s1-s2s3-s2-s4
Alexander polynomial = t^5-7t^4+18t^3-18t^2+7t-1

-- L9(26)-b
s1s2s2-s3s2s2-s1s3-s2s3-s2s3
Alexander polynomial = -2t^5+9t^4-15t^3+15t^2-9t+2

-- L9(27)-a
s1s1s1s2-s3s2s2s1-s3-s2
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(27)-b
s1s2-s3s2s2s2-s1s3-s2s3s3-s2
Alexander polynomial = -2t^5+7t^4-11t^3+11t^2-7t+2

-- L9(28)-a
s1s2-s3s2s2-s1s3-s2-s2s3s3-s2
Alexander polynomial = 2t^5-7t^4+13t^3-13t^2+7t-2

-- L9(28)-b
s1s2-s3s4-s3-s3-s2-s1-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -t^5+7t^4-14t^3+14t^2-7t+1

-- L9(29)     (3,2)(2,2)-a
s1s1-s2-s2s1s1-s2-s2-s2
Alexander polynomial = -t^7+3t^6-7t^5+11t^4-11t^3+7t^2-3t+1

-- L9(29)     (3,2)(2,22-b
s1-s2-s2-s2-s3-s3-s2-s2-s1-s2s3-s2
Alexander polynomial = -3t^5+8t^4-11t^3+11t^2-8t+3

-- L9(30)     (21,2)(2,2)-a
-s1s2s2-s3s2s2s1s2s3s3s3s2
Alexander polynomial = 3t^5-9t^4+14t^3-14t^2+9t-3

-- L9(30)     (21,2)(2,2-b
s1-s2s3s4s3-s2-s1-s2s3s3-s4s3-s2
Alexander polynomial = -t^5+8t^4-17t^3+17t^2-8t+1

-- L9(31)-a
-s1-s1-s1-s1s2-s1s2-s1s2
Alexander polynomial = t^7-4t^6+7t^5-8t^4+8t^3-7t^2+4t-1

-- L9(31)-b
-s1s2-s1s2-s1-s1-s1-s1s2
Alexander polynomial = t^7-4t^6+7t^5-8t^4+8t^3-7t^2+4t-1

-- L9(32)-a
-s1s2-s3s2-s3s2s1-s2s3-s2-s3-s3
Alexander polynomial = -2t^5+9t^4-17t^3+17t^2-9t+2

-- L9(32)-b
s1s2-s3s2-s3s2-s1-s3-s2s3-s2-s3
Alexander polynomial = -2t^5+9t^4-17t^3+17t^2-9t+2

-- L9(33)-a
-s1-s2s3s2-s1s2s2-s1s3-s2s3s2
Alexander polynomial = 2t^5-9t^4+17t^3-17t^2+9t-2

-- L9(33)-b
s1s2-s3s2s2-s1s3-s2s3-s2s3-s2
Alexander polynomial = 2t^5-9t^4+17t^3-17t^2+9t-2

-- L9(34)-a
-s1s2-s3s2s1-s2s3-s2s3s3-s2s3
Alexander polynomial = 2t^5-8t^4+15t^3-15t^2+8t-2

-- L9(34)-b
-s1s2-s1s2-s1-s1-s1s2s2
Alexander polynomial = -t^7+4t^6-8t^5+12t^4-12t^3+8t^2-4t+1

-- L9(35)-a
-s1-s1-s1s2-s1-s1s2-s1s2
Alexander polynomial = t^7-4t^6+8t^5-10t^4+10t^3-8t^2+4t-1

-- L9(35)-b
s1s2-s3s2-s1s3-s2s3-s2s3-s2-s2
Alexander polynomial = -2t^5+8t^4-13t^3+13t^2-8t+2

-- L9(36)-a
-s1s2-s3s2s1-s2s3-s2-s2s3-s2s3
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L9(36)-b
s1s2-s3s2-s1s3-s2s3-s2-s2s3-s2
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L9(37)-a
-s1-s1-s1s2-s1s2s2-s1s2
Alexander polynomial = -t^7+4t^6-8t^5+11t^4-11t^3+8t^2-4t+1

-- L9(37)-b
-s1s2s2-s1s2-s1-s1-s1s2
Alexander polynomial = -t^7+4t^6-8t^5+11t^4-11t^3+8t^2-4t+1

-- L9(38)-a
-s1s2-s3s2s1s1s1s2-s3s2
Alexander polynomial = -2t^5+10t^4-18t^3+18t^2-10t+2

-- L9(38)-b
s1s1-s2-s2-s3s2s1-s2-s3s2-s3-s2
Alexander polynomial = -2t^5+9t^4-19t^3+19t^2-9t+2

-- L9(39)-a
-s1s2s3-s2s3s2-s1-s2s3s3s2s2
Alexander polynomial = -2t^5+9t^4-16t^3+16t^2-9t+2

-- L9(39)-b
-s1s2s2-s1s2-s1-s1s2s2
Alexander polynomial = t^7-4t^6+9t^5-13t^4+13t^3-9t^2+4t-1

-- L9(40)-a
-s1s2-s3s2s1s2s3-s4s3s3s2-s3s4s4s3
Alexander polynomial = -7t^3+18t^2-18t+7

-- L9(40)-b
-s1-s1s2-s1-s1s2-s1-s1s2
Alexander polynomial = t^7-4t^6+9t^5-11t^4+11t^3-9t^2+4t-1

-- L9(41)-a
s1-s2s3s4s3-s2-s1-s2s3-s4s3-s2s3
Alexander polynomial = -t^5+8t^4-19t^3+19t^2-8t+1

-- L9(41)-b
s1s1-s2s1-s2s1s1-s2-s2
Alexander polynomial = t^7-4t^6+9t^5-14t^4+14t^3-9t^2+4t-1

-- L9(42)-a
-s1s2s3-s2s3s2-s1-s2s3s2-s1s2
Alexander polynomial = 2t^5-10t^4+21t^3-21t^2+10t-2

-- L9(42)-b
-s1-s1s2-s1s2-s1s2-s1s2
Alexander polynomial = -t^7+5t^6-11t^5+16t^4-16t^3+11t^2-5t+1

-- L9(43)-a
s1s1s1s1s1-s2-s1-s1-s2
Alexander polynomial = t^5-t^4+t-1

-- L9(43)-b
s1s2s2s1s2s2s2s2s2
Alexander polynomial = -t^7+t^6-t+1

-- L9(44)-a
s1s1-s2-s1-s1-s2-s2-s2-s2
Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1

-- L9(44)-b
s1-s2-s3-s3-s3-s3-s3-s2-s1s2s3s2
Alexander polynomial = t^5-3t^4+4t^3-4t^2+3t-1

-- L9(45)-a
-s1s2-s3s2s1s3s3-s2-s3-s3-s2s3
Alexander polynomial = -2t^3+4t^2-4t+2

-- L9(45)-b
s1s2-s3s2-s1s3s3s3s2s3s3s2
Alexander polynomial = 2t^5-3t^4+t^3-t^2+3t-2

-- L9(46)-a
-s1s2s2-s3-s2-s2s1-s2s3-s2-s3-s3
Alexander polynomial = 2t^3-6t^2+6t-2

-- L9(46)-b
s1-s2-s3s4-s3-s3-s2-s1s2s3s2-s4-s4
Alexander polynomial = -2t^3+6t^2-6t+2

-- L9(47)-a
-s1-s2-s2-s3-s3s2s2s1-s2s3-s2-s3
Alexander polynomial = t^3-3t^2+3t-1

-- L9(47)-b
-s1-s2-s2-s2-s3s4s3s2s1-s2-s2s3-s4-s3s2
Alexander polynomial = -t^3+3t^2-3t+1

-- L9(48)-a
-s1s2s2-s3s2s1s3-s2-s3-s3-s2s3
Alexander polynomial = -3t^3+7t^2-7t+3

-- L9(48)-b
s1s2s2s1s2s3s3-s2s3s2
Alexander polynomial = 2t^5-4t^4+4t^3-4t^2+4t-2

-- L9(49)-a
s1s2s2s2s1s2s2s2s2
Alexander polynomial = -t^7+t^6-t^4+t^3-t+1

-- L9(49)-b
-s1-s2-s2-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -t^3+1

-- L9(50)-a
s1s1s1s1-s2-s1-s1-s2-s2
Alexander polynomial = -t^5+2t^4-2t^3+2t^2-2t+1

-- L9(50)-b
s1-s2s3s4-s3s2-s3-s2-s1s2-s4-s3-s3-s3s2
Alexander polynomial = -t^3+4t^2-4t+1

-- L9(51)-a
s1s2-s3s2-s1s3s3s2s3s3s3s2
Alexander polynomial = 2t^5-3t^4+2t^3-2t^2+3t-2

-- L9(51)-b
s1s1s1-s2-s1-s1-s2-s2-s2
Alexander polynomial = t^5-2t^4+4t^3-4t^2+2t-1

-- L9(52)-a
-s1s2-s3s2s1s3-s2-s3-s3-s2-s2s3
Alexander polynomial = 3t^3-8t^2+8t-3

-- L9(52)-b
s1-s2-s3-s3-s3-s3-s2-s2-s1s2s3s2
Alexander polynomial = t^5-4t^4+6t^3-6t^2+4t-1

-- L9(53)-a
s1s1s2s2s2s1s2s2s2
Alexander polynomial = -t^7+t^6-2t^4+2t^3-t+1

-- L9(53)-b
-s1-s2-s3-s3-s4s3s2s1-s3s4-s3s2-s3s4-s3-s2-s4
Alexander polynomial = t^3+t^2-t-1

-- L9(54)-a
s1s1s1-s2-s1-s1-s1-s2-s2
Alexander polynomial = t^5-3t^4+5t^3-5t^2+3t-1

-- L9(54)-b
-s1-s2s3-s4s3s2s1-s3s4s3s3s2-s3s4-s3-s2-s4
Alexander polynomial = 2t^3-7t^2+7t-2

-- L9(55)     (3,2)(2,2-)-a
s1s1-s2-s2-s1-s1-s2-s2-s2
Alexander polynomial = -t^5+4t^4-7t^3+7t^2-4t+1

-- L9(55)     (3,2)(2,22-b
s1-s2-s2-s2-s3-s3-s2-s2-s1s2s3s2
Alexander polynomial = t^5-4t^4+7t^3-7t^2+4t-1

-- L9(56)     (21,2)(2,2-)-a
-s1-s2-s2-s3s2s2s1s2s3s3s3s2
Alexander polynomial = -t^5+4t^4-7t^3+7t^2-4t+1

-- L9(56)     (21,2)(2,2-b
s1-s2s3s4s3-s2-s1s2s3s3-s4s3s2
Alexander polynomial = t^5-4t^4+7t^3-7t^2+4t-1

-- L9(57)     (3,2-)(2,2)-a
s1s1s2s2s1s1-s2-s2-s2
Alexander polynomial = -t^5+3t^4-6t^3+6t^2-3t+1

-- L9(57)     (3,2-)(2,2-b
s1-s2-s2-s2-s3-s3s2s2-s1-s2s3-s2
Alexander polynomial = t^5-4t^4+5t^3-5t^2+4t-1

-- L9(58)     (21,2-)(2,2)-a
-s1s2s2-s3s2s2s1-s2s3s3s3-s2
Alexander polynomial = -t^5+5t^4-8t^3+8t^2-5t+1

-- L9(58)     (21,2-)(22-b
s1-s2-s3s4s3-s2-s1-s2s3s3-s4-s3-s2
Alexander polynomial = t^5-4t^4+9t^3-9t^2+4t-1

-- L9(59)     (3,2)-(2,2)-a
-s1-s1-s2-s2-s1-s1-s2-s2-s2
Alexander polynomial = t^7-t^6-t^5+3t^4-3t^3+t^2+t-1

-- L9(59)     (3,2)-(2,2-b
s1-s2-s2-s2-s3-s2-s2-s1s2s3s3s2
Alexander polynomial = t^5-3t^3+3t^2-1

-- L9(60)     (21,2)-(2,2)-a
-s1-s2-s2-s3-s2-s2s1s2s3s3s3s2
Alexander polynomial = -t^5+t^4-t+1

-- L9(60)     (21,2)-(22-b
s1s2s3s4s3s2-s1s2s3s3-s4s3s2
Alexander polynomial = -t^5+3t^3-3t^2+1

-- L9(61)-a
s1s2s3s4s3s2-s1s2s3-s4s3s2s3
Alexander polynomial = -t^5+t^3-t^2+1

-- L9(61)-b
-s1-s1-s2s1-s2-s1-s1-s2-s2
Alexander polynomial = t^5-t^3+t^2-1


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