Links with 5 components and 10 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(5)10(1)-a
-s1-s2-s3s4s4-s3s2s1-s3s2-s3s4s4-s3-s2-s3
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-b
-s1-s2s3s3-s2s1-s2-s4s3s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-c
-s1-s2s3s3s4s3s3s2s1-s2s3s3-s2-s4s3s3
Alexander polynomial = -2t^6+9t^5-18t^4+22t^3-18t^2+9t-2

-- L(5)10(1)-d
s1-s2s3s3-s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-e
-s1-s2s3s3-s2s1s4s3s3s2s3s3-s4s3s3-s2
Alexander polynomial = -2t^6+9t^5-18t^4+22t^3-18t^2+9t-2

-- L(5)10(1)-f
-s1s2s2-s3s4s3s2s2s1s2s2-s3s2s2-s4-s3
Alexander polynomial = -2t^6+9t^5-18t^4+22t^3-18t^2+9t-2

-- L(5)10(1)-g
-s1s2s2s3s2s2s1s4-s3s2s2-s3-s4-s3s2s2
Alexander polynomial = -2t^6+9t^5-18t^4+22t^3-18t^2+9t-2

-- L(5)10(1)-h
s1s2-s3s4s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-i
-s1-s2s3s3-s2s1-s2-s4s3s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-j
s1-s2s3s3-s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-k
-s1s2s2s3s2s2s1s2s2-s3-s4-s3s2s2-s3s4
Alexander polynomial = -2t^6+9t^5-18t^4+22t^3-18t^2+9t-2

-- L(5)10(1)-l
s1s2-s3s4s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-m
s1-s2s3s3-s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-n
s1s2-s3s4s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-o
s1s2-s3s4s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = -t^6+7t^5-19t^4+26t^3-19t^2+7t-1

-- L(5)10(1)-p
s1s2s3-s4-s5-s5-s4-s3-s2-s1-s4-s3-s2-s4-s3-s4s5-s4s3s2-s4s3-s4
Alexander polynomial = -5t^4+20t^3-30t^2+20t-5

-- L(5)10(2)-a
-s1-s2-s3s4s4-s3s2s1-s3s2-s3-s4-s4-s3-s2-s3
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(5)10(2)-b
-s1-s2s3s3-s2s1-s2s4s3s3-s2s4
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-c
-s1-s2-s3-s3s4s3s3s2s1-s2s3s3-s2-s4s3s3
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-d
s1-s2s3s3-s2-s1s2-s4s3s3s2-s4
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-e
-s1-s2-s3-s3-s2s1s4s3s3s2s3s3-s4s3s3-s2
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-f
-s1s2s2s3s4s3s2s2s1s2s2-s3s2s2-s4s3
Alexander polynomial = 2t^6-7t^5+10t^4-10t^3+10t^2-7t+2

-- L(5)10(2)-g
-s1-s2-s2s3s2s2s1s4-s3s2s2-s3-s4-s3s2s2
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-h
s1s2-s3s4s4-s3-s2-s1-s3-s2s3s4s4s3s2-s3
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-i
-s1-s2s3s3-s2s1-s2-s4-s3-s3-s2-s4
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(5)10(2)-j
s1s2s3s3s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-k
-s1-s2-s2s3s2s2s1s2s2-s3-s4-s3s2s2-s3s4
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-l
s1s2-s3s4s4-s3-s2-s1s3-s2-s3s4s4-s3s2s3
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-m
s1-s2-s3-s3-s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(5)10(2)-n
s1s2s3s4s4s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = t^6-5t^5+11t^4-14t^3+11t^2-5t+1

-- L(5)10(2)-o
s1s2-s3-s4-s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(5)10(2)-p
s1s2s3s4-s5-s5s4-s3-s2-s1-s4-s3-s2-s4-s3-s4s5-s4s3s2-s4s3-s4
Alexander polynomial = 3t^4-12t^3+18t^2-12t+3

-- L(5)10(3)-a
-s1-s2-s3s4s4-s3s2s1-s3s2s3-s4-s4s3-s2-s3
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-b
-s1-s2s3s3-s2s1-s2s4-s3-s3-s2s4
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-c
-s1-s2-s3-s3s4-s3-s3s2s1-s2s3s3-s2-s4s3s3
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-d
s1s2s3s3s2-s1s2-s4s3s3s2-s4
Alexander polynomial = -t^6+3t^5-3t^4+2t^3-3t^2+3t-1

-- L(5)10(3)-e
-s1s2-s3-s3s2s1s4s3s3s2s3s3-s4s3s3-s2
Alexander polynomial = -t^6+3t^5-3t^4+2t^3-3t^2+3t-1

-- L(5)10(3)-f
-s1-s2-s2s3s4s3s2s2s1s2s2-s3s2s2-s4s3
Alexander polynomial = -t^6+3t^5-3t^4+2t^3-3t^2+3t-1

-- L(5)10(3)-g
-s1-s2-s2s3-s2-s2s1s4-s3s2s2-s3-s4-s3s2s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-h
s1s2-s3s4s4-s3-s2-s1s3-s2s3s4s4s3s2s3
Alexander polynomial = -t^6+3t^5-3t^4+2t^3-3t^2+3t-1

-- L(5)10(3)-i
-s1-s2s3s3-s2s1s2-s4-s3-s3s2-s4
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-j
s1s2-s3-s3s2-s1-s2-s4s3s3-s2-s4
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-k
-s1-s2-s2s3-s2-s2s1s2s2-s3-s4-s3s2s2-s3s4
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-l
s1s2s3s4s4s3-s2-s1s3-s2-s3s4s4-s3s2s3
Alexander polynomial = -t^6+3t^5-3t^4+2t^3-3t^2+3t-1

-- L(5)10(3)-m
s1-s2-s3-s3-s2-s1-s2s4s3s3-s2s4
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-n
s1s2s3-s4-s4s3-s2-s1-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(5)10(3)-o
s1s2-s3-s4-s4-s3-s2-s1-s3-s2-s3-s4-s4-s3s2-s3
Alexander polynomial = t^6-t^5-5t^4+10t^3-5t^2-t+1

-- L(5)10(3)-p
s1s2s3s4-s5-s5s4-s3-s2-s1s4-s3-s2-s4-s3-s4s5-s4s3s2-s4s3s4
Alexander polynomial = -t^4+4t^3-6t^2+4t-1


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