Links with 4 components and at most 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



-- L(4)8(1)-a
-s1-s2s3s3-s2s1-s2s3s3-s2
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-b
-s1s2s2-s1-s3s2s2-s3
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-c
-s1s2s2s3s2s2s1s2s2-s3s2s2
Alexander polynomial = 2t^5-6t^4+8t^3-8t^2+6t-2

-- L(4)8(1)-d
s1-s2s3s3-s2-s1-s2s3s3-s2
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-e
-s1s2s2-s1-s3s2s2-s3
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-f
s1-s2s3s3-s2-s1-s2s3s3-s2
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-g
s1-s2s3s3-s2-s1-s2s3s3-s2
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L(4)8(1)-h
s1s2-s3-s4-s4-s3-s2-s1-s3-s2-s3s4-s3s2-s3
Alexander polynomial = 4t^3-12t^2+12t-4

-- L(4)8(2)-a
-s1-s2s3s3-s2s1-s2-s3-s3-s2
Alexander polynomial = 2t^3-6t^2+6t-2

-- L(4)8(2)-b
s1s2s2s1-s3s2s2-s3
Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1

-- L(4)8(2)-c
-s1-s2-s2s3s2s2s1s2s2-s3s2s2
Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1

-- L(4)8(2)-d
s1-s2s3s3-s2-s1s2s3s3s2
Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1

-- L(4)8(2)-e
-s1-s2-s2-s1-s3s2s2-s3
Alexander polynomial = 2t^3-6t^2+6t-2

-- L(4)8(2)-f
s1s2s3s3s2-s1-s2s3s3-s2
Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1

-- L(4)8(2)-g
s1-s2-s3-s3-s2-s1-s2s3s3-s2
Alexander polynomial = 2t^3-6t^2+6t-2

-- L(4)8(2)-h
s1s2s3-s4-s4s3-s2-s1-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -2t^3+6t^2-6t+2

-- L(4)8(3)-a
-s1-s2s3s3-s2s1s2-s3-s3s2
Alexander polynomial = 0

-- L(4)8(3)-b
s1-s2-s2s1-s3s2s2-s3
Alexander polynomial = 0

-- L(4)8(3)-c
-s1-s2-s2s3-s2-s2s1s2s2-s3s2s2
Alexander polynomial = 0

-- L(4)8(3)-d
s1s2s3s3s2-s1s2s3s3s2
Alexander polynomial = t^5-t^4-2t^3+2t^2+t-1

-- L(4)8(3)-e
s1s2s2s1-s3-s2-s2-s3
Alexander polynomial = 0

-- L(4)8(3)-f
s1s2-s3-s3s2-s1-s2s3s3-s2
Alexander polynomial = 0

-- L(4)8(3)-g
s1-s2-s3-s3-s2-s1-s2-s3-s3-s2
Alexander polynomial = -t^5+t^4+2t^3-2t^2-t+1

-- L(4)8(3)-h
s1s2s3-s4-s4s3-s2-s1s3-s2-s3s4-s3s2s3
Alexander polynomial = 0

-- L(4)9(1)-a
-s1-s2-s3s4s4-s3s2s1-s3s2-s3s4-s3-s2-s3
Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1

-- L(4)9(1)-b
-s1s2s2-s1-s3s2s2s3s3s3
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L(4)9(1)-c
-s1s2s2-s3s2s2s1-s2s3s3-s2s3
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L(4)9(1)-d
s1s1-s2s1s1-s3s2s2-s3s2
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L(4)9(1)-e
-s1-s2s3s3-s2s1-s2-s4s3-s2-s4
Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1

-- L(4)9(1)-f
s1s2s2-s3s2s2-s1s3-s2s3s3-s2
Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2

-- L(4)9(1)-g
s1-s2s3-s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1

-- L(4)9(1)-h
s1s2-s3s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1


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