Knots with 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



-- 9(1)
-s1-s1-s1-s1-s1-s1-s1-s1-s1
Alexander polynomial = -t^8+t^7-t^6+t^5-t^4+t^3-t^2+t-1

-- 9(2)
s1-s2s3s4-s3s2-s3-s2-s1s2-s4-s3-s2-s2-s2-s3
Alexander polynomial = 4t^2-7t+4

-- 9(3)
s1s1s1s1s1s1s1s2-s1s2
Alexander polynomial = 2t^6-3t^5+3t^4-3t^3+3t^2-3t+2

-- 9(4)
s1s2-s3-s2-s2-s2-s2-s2-s1-s3-s2s3-s2
Alexander polynomial = -3t^4+5t^3-5t^2+5t-3

-- 9(5)
s1s2s3s3s4-s3-s2-s1s3s3s2s3-s4s3-s2s4-s3s4
Alexander polynomial = 6t^2-11t+6

-- 9(6)
s1-s2-s1-s1-s1-s1-s1-s1-s2-s2
Alexander polynomial = 2t^6-4t^5+5t^4-5t^3+5t^2-4t+2

-- 9(7)
-s1-s2-s2-s2-s2-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = -3t^4+7t^3-9t^2+7t-3

-- 9(8)
s1s2s3-s4s3-s2-s1s4-s3-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -2t^4+8t^3-11t^2+8t-2

-- 9(9)
s1-s2-s1-s1-s1-s1-s1-s2-s2-s2
Alexander polynomial = 2t^6-4t^5+6t^4-7t^3+6t^2-4t+2

-- 9(10)
s1s2-s3s2-s1s3s2s2s3-s2s3s3s3
Alexander polynomial = -4t^4+8t^3-9t^2+8t-4

-- 9(11)
-s1s2s2s2s2-s3s2s1s2-s3s2
Alexander polynomial = t^6-5t^5+7t^4-7t^3+7t^2-5t+1

-- 9(12)
s1-s2s3s4-s3s2-s3-s2-s1-s2-s4s3-s2-s2
Alexander polynomial = -2t^4+9t^3-13t^2+9t-2

-- 9(13)
s1s2-s3s2-s1s3-s2s3s2s2s2s2s3
Alexander polynomial = -4t^4+9t^3-11t^2+9t-4

-- 9(14)
-s1s2-s3s2s1s2-s3s4s3-s2s3s2-s4-s3
Alexander polynomial = 2t^4-9t^3+15t^2-9t+2

-- 9(15)
-s1s2-s3s2s1s2s2-s3s4s3-s2s3s2-s4
Alexander polynomial = -2t^4+10t^3-15t^2+10t-2

-- 9(16)
s1s1s1s1s2s2-s1s2s2s2
Alexander polynomial = 2t^6-5t^5+8t^4-9t^3+8t^2-5t+2

-- 9(17)
-s1s2-s3s2s1-s3-s3-s3s2-s3s2
Alexander polynomial = -t^6+5t^5-9t^4+9t^3-9t^2+5t-1

-- 9(18)
-s1-s3-s3s2-s3-s2-s2-s2s1-s2s3-s2-s3
Alexander polynomial = -4t^4+10t^3-13t^2+10t-4

-- 9(19)
-s1s2-s3s4-s3-s2s1-s4s3s2-s4s3-s4s3-s2s3
Alexander polynomial = 2t^4-10t^3+17t^2-10t+2

-- 9(20)
s1-s2s3-s2-s2-s1-s2-s2-s2s3-s2
Alexander polynomial = t^6-5t^5+9t^4-11t^3+9t^2-5t+1

-- 9(21)
-s1-s2s3s2s2-s4-s3s2s1s2-s3s2s4s3
Alexander polynomial = -2t^4+11t^3-17t^2+11t-2

-- 9(22)
s1-s2s3s3s3-s2-s1-s2s3-s2s3
Alexander polynomial = -t^6+5t^5-10t^4+11t^3-10t^2+5t-1

-- 9(23)
s1-s2-s1-s1-s1-s2-s2-s3-s3s2-s3
Alexander polynomial = -4t^4+11t^3-15t^2+11t-4

-- 9(24)
-s1-s2-s2s3s3s3-s2s1-s2s3-s2
Alexander polynomial = t^6-5t^5+10t^4-13t^3+10t^2-5t+1

-- 9(25)
s1-s2-s3-s3-s3-s2-s1s3s4-s3-s2s3-s2s4
Alexander polynomial = -3t^4+12t^3-17t^2+12t-3

-- 9(26)
-s1s2s2s2-s3s2s1-s3s2-s3s2
Alexander polynomial = -t^6+5t^5-11t^4+13t^3-11t^2+5t-1

-- 9(27)
s1-s2s3-s2-s2-s1-s2s3-s2s3s3
Alexander polynomial = t^6-5t^5+11t^4-15t^3+11t^2-5t+1

-- 9(28)
s1-s2s3-s2-s2-s1-s2-s2s3s3-s2
Alexander polynomial = -t^6+5t^5-12t^4+15t^3-12t^2+5t-1

-- 9(29)
s1-s2s3-s2-s2s1-s2s3-s2
Alexander polynomial = -t^6+5t^5-12t^4+15t^3-12t^2+5t-1

-- 9(30)
-s1s2-s3s2-s1s2s2-s1-s3
Alexander polynomial = t^6-5t^5+12t^4-17t^3+12t^2-5t+1

-- 9(31)
s1-s2s3-s2-s2-s1-s2-s2s3-s2s3
Alexander polynomial = -t^6+5t^5-13t^4+17t^3-13t^2+5t-1

-- 9(32)
-s1s2-s1-s3s2-s3s2-s3-s3
Alexander polynomial = -t^6+6t^5-14t^4+17t^3-14t^2+6t-1

-- 9(33)
-s1-s2s3-s2s3s3-s2s1-s2s3-s2
Alexander polynomial = t^6-6t^5+14t^4-19t^3+14t^2-6t+1

-- 9(34)
-s1s2-s3s2-s1s2-s1-s3s2
Alexander polynomial = t^6-6t^5+16t^4-23t^3+16t^2-6t+1

-- 9(35)
-s1-s2-s3-s3-s4s3s2s1-s3-s3-s4s3s2-s3s4-s3-s2-s4
Alexander polynomial = 7t^2-13t+7

-- 9(36)
-s1s2-s3s2s1s2s2s2-s3s2s2
Alexander polynomial = t^6-5t^5+8t^4-9t^3+8t^2-5t+1

-- 9(37)
-s1-s2s3-s4s3s2s1s3-s4s3s2-s3s4-s3-s2-s4
Alexander polynomial = 2t^4-11t^3+19t^2-11t+2

-- 9(38)
-s1s2s3-s2s3s2s2s1s1s2s2s3-s2
Alexander polynomial = -5t^4+14t^3-19t^2+14t-5

-- 9(39)
-s1s2-s3s2s1s2s3-s4s3s3s2-s3-s4s3
Alexander polynomial = -3t^4+14t^3-21t^2+14t-3

-- 9(40)
-s1s2-s1-s3s2-s1-s3s2-s3
Alexander polynomial = -t^6+7t^5-18t^4+23t^3-18t^2+7t-1

-- 9(41)
-s1s2-s3s2s4-s3s2s1-s2-s2-s3-s4-s3s2
Alexander polynomial = 3t^4-12t^3+19t^2-12t+3

-- 9(42)
-s1s2-s3s2s1s2s2s2-s3-s2-s2
Alexander polynomial = t^4-2t^3+t^2-2t+1

-- 9(43)
s1s2s3s3s3s2-s1-s2s3-s2s3
Alexander polynomial = t^6-3t^5+2t^4-t^3+2t^2-3t+1

-- 9(44)
s1s2-s3-s3-s3s2-s1s3s4-s3-s2s3-s2s4
Alexander polynomial = t^4-4t^3+7t^2-4t+1

-- 9(45)
-s1s2-s3s2-s1-s2-s2-s1-s3
Alexander polynomial = t^4-6t^3+9t^2-6t+1

-- 9(46)
-s1-s2-s3s4s3s3s2s1-s3-s3-s4s3s2-s3s4-s3-s2-s4
Alexander polynomial = -2t^2+5t-2

-- 9(47)
-s1s2-s1s3s2-s1s2s3s2
Alexander polynomial = -t^6+4t^5-6t^4+5t^3-6t^2+4t-1

-- 9(48)
-s1-s2s3-s4s3s2s1s3-s4s3s2s3-s4s3-s2s4
Alexander polynomial = -t^4+7t^3-11t^2+7t-1

-- 9(49)
s1s2s2s3-s4s3-s2-s1s2s3s2s4s3s2
Alexander polynomial = 3t^4-6t^3+7t^2-6t+3


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