Non-alternating knots with 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



Output from braid v5.0.b1

-- 10(1I)
s1s1s1s1s1-s2-s1-s1-s2-s2
Alexander polynomial = t^6-2t^5+2t^4-t^3+2t^2-2t+1

-- 10(1II)
-s1s2-s3s2s1s3s3-s2-s3-s3-s2-s2s3
Alexander polynomial = -2t^4+6t^3-9t^2+6t-2

-- 10(1III)
-s1-s2s3-s4s3s2s1s3-s4-s3-s3s2-s3-s4s3s2-s3s4
Alexander polynomial = 2t^4-8t^3+13t^2-8t+2

-- 10(1IV)
-s1s2s2-s3s2s1s3-s2-s3-s3-s2-s2s3
Alexander polynomial = -3t^4+9t^3-13t^2+9t-3

-- 10(1V)
-s1s2s3-s2s3s2-s1-s2s3s2-s1-s2-s2
Alexander polynomial = -3t^4+11t^3-17t^2+11t-3

-- 10(1VI)
s1s2-s3s2-s1-s2-s2-s2s3s3s3-s2-s2
Alexander polynomial = -t^6+t^5+t^4-3t^3+t^2+t-1

-- 10(2I)
s1s1s1s1-s2-s1-s1-s1-s2-s2
Alexander polynomial = -t^6+3t^5-4t^4+5t^3-4t^2+3t-1

-- 10(2II)
-s1-s2s3-s4s3s2s1s3s3-s4s3s2-s3-s3-s4s3-s2s4
Alexander polynomial = -2t^4+7t^3-9t^2+7t-2

-- 10(2III)
-s1s2-s3s2s1s3-s2-s3-s3-s3-s2-s2s3
Alexander polynomial = 3t^4-10t^3+13t^2-10t+3

-- 10(2IV)
s1-s2-s3-s3-s4s3-s2-s1s3-s2s4s3-s2s3
Alexander polynomial = t^4-6t^3+11t^2-6t+1

-- 10(2V)
-s1-s2s3-s4s3s2s1s3s2-s3-s3-s4-s5s4s3-s2s3s4s5
Alexander polynomial = t^4-4t^3+5t^2-4t+1

-- 10(2VI)
s1s2s3-s4s3s2-s1-s2-s4s3-s2s3
Alexander polynomial = t^6-5t^5+8t^4-7t^3+8t^2-5t+1

-- 10(2VII)
s1s1s1s2-s1-s1s2-s1-s1s2
Alexander polynomial = -t^6+3t^5-5t^4+7t^3-5t^2+3t-1

-- 10(2VIII)
-s1s2-s3s2s1s2-s3-s3s2-s3-s3s2s3
Alexander polynomial = t^6-4t^5+10t^4-15t^3+10t^2-4t+1

-- 10(2IX)
s1s2-s3s2-s1s3-s2-s2-s3s2-s3-s2-s2
Alexander polynomial = 3t^4-9t^3+11t^2-9t+3

-- 10(3I)
s1s1s1-s2-s1-s1-s2-s2-s2-s2
Alexander polynomial = t^6-2t^5+4t^4-5t^3+4t^2-2t+1

-- 10(3II)
-s1-s2-s2-s2-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -t^4+2t^3-3t^2+2t-1

-- 10(3III)
s1s1s1-s2-s1-s1-s1-s2-s2-s2
Alexander polynomial = t^6-3t^5+6t^4-7t^3+6t^2-3t+1

-- 10(3IV)
-s1s2s2s2-s3-s2-s2s1-s2s3-s2-s3-s3
Alexander polynomial = -2t^4+4t^3-5t^2+4t-2

-- 10(3V)
-s1-s2-s2-s3-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -t^4+t^3-t^2+t-1

-- 10(3VI)
-s1s2-s3s2s1s2-s3s2-s3s2-s3s2s3
Alexander polynomial = -t^6+5t^5-12t^4+15t^3-12t^2+5t-1

-- 10(3VII)
s1s1s1-s2-s2-s1-s1-s2-s2-s2
Alexander polynomial = t^6-3t^5+7t^4-9t^3+7t^2-3t+1

-- 10(3VIII)
-s1s2-s1s2s2-s1-s1-s2-s2-s2
Alexander polynomial = t^6-4t^5+9t^4-11t^3+9t^2-4t+1

-- 10(3IX)
s1-s2s3s4s3-s2-s2-s1s2s3s3-s4s3s2
Alexander polynomial = t^6-4t^5+10t^4-13t^3+10t^2-4t+1

-- 10(3X)
-s1-s2s3-s2s3s3-s2-s2s1-s2s3-s2-s3
Alexander polynomial = -t^6+4t^5-8t^4+9t^3-8t^2+4t-1

-- 10(4I)
s1-s2-s3-s3-s3-s3-s3-s2-s2-s1s2s3s2
Alexander polynomial = t^6-4t^5+6t^4-7t^3+6t^2-4t+1

-- 10(4II)
s1s2-s3-s3-s3s2-s1s4-s3s2-s3-s2-s4-s2s3-s2
Alexander polynomial = -2t^4+8t^3-11t^2+8t-2

-- 10(4III)
s1s2-s3-s3-s3s2-s1s3s4-s3-s2s3-s2-s4-s4-s4
Alexander polynomial = -t^4+5t^3-7t^2+5t-1

-- 10(4IV)
s1s1s2s3-s2s3s2-s1-s2s3s2-s1s2
Alexander polynomial = 2t^4-10t^3+15t^2-10t+2

-- 10(4V)
s1s2-s3s2-s1s3s2s2-s3s2-s3s2s2
Alexander polynomial = t^6-4t^5+4t^4-3t^3+4t^2-4t+1

-- 10(4VI)
-s1-s2-s2-s3s2s2s2s1s2s3s3s3s2
Alexander polynomial = t^6-4t^5+6t^4-7t^3+6t^2-4t+1

-- 10(4VII)
s1s1s2s2s2s1s1-s2s1-s2
Alexander polynomial = -t^6+6t^5-11t^4+13t^3-11t^2+6t-1

-- 10(4VIII)
s1s2-s3-s3-s3s2-s1-s2-s2-s2s3-s2-s2
Alexander polynomial = t^6-5t^5+9t^4-11t^3+9t^2-5t+1

-- 10(5I)
-s1-s2-s3s4s3-s2s1-s4-s3-s3-s3s2-s3s4-s3-s2-s4s3
Alexander polynomial = t^4+t^3-3t^2+t+1

-- 10(5II)
-s1-s1-s2s1-s2-s1-s1-s2-s2-s2
Alexander polynomial = t^6-2t^4+3t^3-2t^2+1

-- 10(6I)
s1s2s2s2s1s2s2s2s2s2
Alexander polynomial = t^8-t^7+t^5-t^4+t^3-t+1

-- 10(6II)
s1s2-s3s2-s1s3s3s2s3s3s3s2s2
Alexander polynomial = -2t^6+3t^5-2t^4+t^3-2t^2+3t-2

-- 10(6III)
s1s1s2s2s2s2s1s2s2s2
Alexander polynomial = t^8-t^7+2t^5-3t^4+2t^3-t+1

-- 10(6IV)
s1s2-s3s2-s1s3s3s3s2s3s3s3s2
Alexander polynomial = -2t^6+3t^5-t^4-t^3-t^2+3t-2

-- 10(6V)
s1s2s2s2s1s2s3s3-s2s3s2
Alexander polynomial = -2t^6+4t^5-4t^4+3t^3-4t^2+4t-2

-- 10(6VII)
s1s2s3s4s3s2s2-s1s2s3s3-s4s3s2
Alexander polynomial = t^6-4t^4+7t^3-4t^2+1

-- 10(6VIII)
-s1-s1-s1-s2-s2-s1-s1-s2-s2-s2
Alexander polynomial = t^8-t^7-t^6+4t^5-5t^4+4t^3-t^2-t+1


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