## 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

```