braid results

## 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

```
-- 10(1)
-s1s2-s3s2s4-s3s2s1-s3s2-s3s2-s4-s3
Alexander polynomial = -t^6+7t^5-21t^4+31t^3-21t^2+7t-1

-- 10(2)
-s1-s2s3s3-s4s3s2s1s3-s4s3s2s3-s4s3-s2
Alexander polynomial = t^6-7t^5+21t^4-29t^3+21t^2-7t+1

-- 10(3)
-s1s2-s3s2s1s2-s3s2s4-s3s2-s3-s3-s4
Alexander polynomial = -t^6+7t^5-19t^4+27t^3-19t^2+7t-1

-- 10(4)
-s1-s2-s2s3-s4s3-s2s1-s2s3-s2-s4
Alexander polynomial = t^6-7t^5+20t^4-27t^3+20t^2-7t+1

-- 10(5)
-s1s2s2-s3s2s1s3-s2s3s3-s2-s2s3
Alexander polynomial = -2t^6+8t^5-18t^4+23t^3-18t^2+8t-2

-- 10(6)
-s1-s2s3s3s2-s1s2s2-s1s3-s2s3s2
Alexander polynomial = -2t^6+9t^5-20t^4+25t^3-20t^2+9t-2

-- 10(7)
s1-s2s3-s4s3-s2-s1s3-s2-s2s4s3s3-s2
Alexander polynomial = -t^6+7t^5-18t^4+25t^3-18t^2+7t-1

-- 10(8)
-s1-s1s2s3-s2s3s2s2-s1s2s2s3-s2
Alexander polynomial = -2t^6+9t^5-21t^4+27t^3-21t^2+9t-2

-- 10(9)
s1-s2s3s4s3-s2-s2-s1-s2s3s3-s4s3-s2
Alexander polynomial = -t^6+8t^5-20t^4+27t^3-20t^2+8t-1

-- 10(10)
-s1s2-s3s2s4-s3s2s1s2-s3-s4-s3-s3s2
Alexander polynomial = -t^6+8t^5-22t^4+31t^3-22t^2+8t-1

-- 10(11)
-s1s2-s1-s1s2s3s3-s2s3s2s2
Alexander polynomial = -2t^6+8t^5-17t^4+21t^3-17t^2+8t-2

-- 10(12)
-s1s2-s3s4-s3-s2s1-s3s4-s3s2-s3s4-s3-s2-s3
Alexander polynomial = t^6-8t^5+24t^4-33t^3+24t^2-8t+1

-- 10(13)
-s1-s2s3-s4s3s2s1s3-s2-s4s3-s4s3-s2
Alexander polynomial = -t^6+8t^5-24t^4+35t^3-24t^2+8t-1

-- 10(14)
-s1s2s2-s3s2s1s2-s3s4-s3s2-s3-s3-s4
Alexander polynomial = -t^6+7t^5-17t^4+23t^3-17t^2+7t-1

-- 10(15)
s1-s2-s2s3s3s4-s3s2-s3-s2-s1s2-s4-s3s2s3
Alexander polynomial = 4t^4-13t^3+19t^2-13t+4

-- 10(16)
-s1s2-s1-s1s2s3s3s3-s2s3s2
Alexander polynomial = -2t^6+8t^5-16t^4+19t^3-16t^2+8t-2

-- 10(17)
-s1s2-s3-s3s2-s3s2s1-s2s3-s2-s3-s3
Alexander polynomial = -2t^6+9t^5-19t^4+23t^3-19t^2+9t-2

-- 10(18)
-s1s2-s3s2s1s3s3-s2s3s3-s2-s2s3
Alexander polynomial = -2t^6+7t^5-15t^4+19t^3-15t^2+7t-2

-- 10(19)
s1s1s1s2-s3s2s2s1-s3-s3-s2
Alexander polynomial = -2t^6+7t^5-14t^4+17t^3-14t^2+7t-2

-- 10(20)
s1s2-s3s2-s1s3s3s3s3-s2s3-s2-s2
Alexander polynomial = -2t^6+7t^5-13t^4+15t^3-13t^2+7t-2

-- 10(21)
s1s2-s3s2-s1s3s3s4-s3s2-s3-s2-s4s3-s2-s2
Alexander polynomial = 4t^4-14t^3+21t^2-14t+4

-- 10(22)
-s1-s2s3-s2s1-s3-s3s2-s3s2s4s3-s2s3s2-s4
Alexander polynomial = 4t^4-16t^3+25t^2-16t+4

-- 10(23)
s1s2-s3s2-s1s3s3-s2s3s3s3-s2-s2
Alexander polynomial = -2t^6+7t^5-14t^4+17t^3-14t^2+7t-2

-- 10(24)
s1s2-s3s2-s1s3-s2-s2s3s3s3s3-s2
Alexander polynomial = -2t^6+6t^5-10t^4+11t^3-10t^2+6t-2

-- 10(25)
-s1s2s3-s2s3s2-s1-s2s3s2-s1s2s2
Alexander polynomial = -2t^6+10t^5-24t^4+31t^3-24t^2+10t-2

-- 10(26)
-s1-s1s2-s1s2s2-s1s2-s1s2
Alexander polynomial = t^8-5t^7+12t^6-19t^5+23t^4-19t^3+12t^2-5t+1

-- 10(27)
-s1-s1s2s2-s1-s1s2s2-s1s2
Alexander polynomial = t^8-4t^7+10t^6-17t^5+21t^4-17t^3+10t^2-4t+1

-- 10(28)
-s1-s2-s2s3-s2s3-s2-s1s2-s1-s2s3s2
Alexander polynomial = -2t^6+11t^5-27t^4+35t^3-27t^2+11t-2

-- 10(29)
-s1s2-s3s2-s3-s4-s3s2s1s2-s3s4-s3s2
Alexander polynomial = -t^6+9t^5-26t^4+37t^3-26t^2+9t-1

-- 10(30)
-s1s2s3s3-s2s3s2-s1-s2s3s2-s1s2
Alexander polynomial = -2t^6+11t^5-26t^4+33t^3-26t^2+11t-2

-- 10(31)
-s1s2s2-s1-s1s2-s1-s1s2s2
Alexander polynomial = t^8-4t^7+10t^6-16t^5+19t^4-16t^3+10t^2-4t+1

-- 10(32)
s1s1-s2s1-s2s1s1-s2-s2-s2
Alexander polynomial = t^8-4t^7+9t^6-15t^5+19t^4-15t^3+9t^2-4t+1

-- 10(33)
-s1s2s2-s1s2-s1-s1-s1s2s2
Alexander polynomial = t^8-4t^7+9t^6-14t^5+17t^4-14t^3+9t^2-4t+1

-- 10(34)
s1s2-s3-s3s2-s3-s3s2-s1-s3-s2s3-s2
Alexander polynomial = -2t^6+8t^5-17t^4+21t^3-17t^2+8t-2

-- 10(35)
s1s1s1-s2-s2s1s1-s2-s2-s2
Alexander polynomial = t^8-3t^7+7t^6-12t^5+15t^4-12t^3+7t^2-3t+1

-- 10(36)
s1s1s1-s2s1s1-s2-s2-s2-s2
Alexander polynomial = t^8-3t^7+6t^6-9t^5+11t^4-9t^3+6t^2-3t+1

-- 10(37)
-s1s2-s1-s1-s1-s1s2s2s2s2
Alexander polynomial = t^8-3t^7+5t^6-7t^5+9t^4-7t^3+5t^2-3t+1

-- 10(38)
-s1s2-s1s2-s1s2-s1s2-s1s2
Alexander polynomial = t^8-6t^7+15t^6-24t^5+29t^4-24t^3+15t^2-6t+1

-- 10(39)
s1-s2s3-s4s3-s2-s1-s2-s4s3-s2s3
Alexander polynomial = -t^6+7t^5-20t^4+29t^3-20t^2+7t-1

-- 10(40)
-s1-s2s3-s4s3s2s1s3-s4s3s2s3-s4s3-s2-s4
Alexander polynomial = -t^6+7t^5-19t^4+27t^3-19t^2+7t-1

-- 10(41)
-s1s2-s3s4-s3s2s1-s3-s3s2-s3s2-s4-s3
Alexander polynomial = t^6-7t^5+17t^4-21t^3+17t^2-7t+1

-- 10(42)
s1-s2s3s3-s4s3-s2-s1s3-s2s4s3-s2s3
Alexander polynomial = t^6-7t^5+18t^4-23t^3+18t^2-7t+1

-- 10(43)
-s1s2-s3s4-s3s2s1-s3s2-s3s2-s4-s3-s3
Alexander polynomial = t^6-7t^5+19t^4-25t^3+19t^2-7t+1

-- 10(44)
-s1s2-s3s2s2s1s1s1s2-s3s2
Alexander polynomial = 2t^6-10t^5+20t^4-25t^3+20t^2-10t+2

-- 10(45)
s1s2-s3s4-s3-s3-s2-s1-s3-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -t^6+7t^5-16t^4+21t^3-16t^2+7t-1

-- 10(46)
s1s2-s3s2s2-s1s3-s2s3-s2s3-s2-s2
Alexander polynomial = 2t^6-9t^5+18t^4-23t^3+18t^2-9t+2

-- 10(47)
-s1-s2s3-s4s3s2s1s3s2-s3-s3-s4-s5-s4s3-s2s3-s4s5
Alexander polynomial = -3t^4+16t^3-27t^2+16t-3

-- 10(48)
s1-s2s1-s2-s3-s3s2-s3-s2-s2-s2
Alexander polynomial = 2t^6-8t^5+13t^4-15t^3+13t^2-8t+2

-- 10(49)
-s1s2-s3-s4s3-s4-s3-s3s2s1-s3s2-s3s4-s3-s2-s4s3
Alexander polynomial = -4t^4+15t^3-21t^2+15t-4

-- 10(50)
s1-s2-s3-s3-s3-s2-s1s3s4-s3-s2s3-s2-s4-s4-s4
Alexander polynomial = 5t^4-15t^3+21t^2-15t+5

-- 10(51)
-s1s2-s3s2s1-s3-s4-s4s3s2-s3s4-s3-s2-s4-s3
Alexander polynomial = -3t^4+13t^3-19t^2+13t-3

-- 10(52)
s1s2s3-s4s3-s2-s1s4-s5s4-s3-s2s4-s3s5s4-s3s2-s3
Alexander polynomial = -2t^4+12t^3-21t^2+12t-2

-- 10(53)
-s1-s2s3-s4s3s2s1-s2s3s3s3-s2-s4s3
Alexander polynomial = t^6-7t^5+16t^4-19t^3+16t^2-7t+1

-- 10(54)
s1s2s2-s3s2-s3s2-s1-s3-s2s3-s2-s3
Alexander polynomial = 2t^6-9t^5+19t^4-25t^3+19t^2-9t+2

-- 10(55)
s1s2s2-s3s2s2s2-s1s3-s2s3-s2s3
Alexander polynomial = 2t^6-9t^5+16t^4-19t^3+16t^2-9t+2

-- 10(56)
s1-s2-s3-s3-s3-s3-s2-s2-s1-s2-s2s3-s2
Alexander polynomial = -3t^6+9t^5-16t^4+19t^3-16t^2+9t-3

-- 10(57)
s1-s2-s3-s3-s3-s2-s1s4-s3s2-s3-s2-s4-s2s3-s2
Alexander polynomial = 6t^4-18t^3+25t^2-18t+6

-- 10(58)
s1s1s1-s2s1-s2-s2-s3-s3s2-s3
Alexander polynomial = 2t^6-8t^5+15t^4-19t^3+15t^2-8t+2

-- 10(59)
s1-s2-s3-s3-s3-s2-s1-s2-s2-s2s3-s2-s2
Alexander polynomial = -3t^6+9t^5-15t^4+17t^3-15t^2+9t-3

-- 10(60)
-s1s2-s3s2s1-s3s2-s3s4-s3-s2-s4-s4s3-s4-s3
Alexander polynomial = -4t^4+17t^3-25t^2+17t-4

-- 10(61)
s1-s2s1-s2-s3-s3-s3s2-s3-s2-s2
Alexander polynomial = 2t^6-8t^5+14t^4-17t^3+14t^2-8t+2

-- 10(62)
-s1s2-s3s4-s3s2s1s2-s3s2-s4-s3-s3-s3
Alexander polynomial = t^6-7t^5+15t^4-17t^3+15t^2-7t+1

-- 10(63)
-s1s2-s3-s4s3s2s1-s4-s3-s3-s3s2-s3s4-s3-s2-s4s3
Alexander polynomial = -4t^4+16t^3-23t^2+16t-4

-- 10(64)
-s1s2s3s3-s2s3s2-s1s2s2s2
Alexander polynomial = 2t^6-8t^5+14t^4-17t^3+14t^2-8t+2

-- 10(65)
-s1s2-s3s4-s3-s2s1-s4-s4-s4s3s2-s3-s3-s4s3-s2s3
Alexander polynomial = -4t^4+14t^3-19t^2+14t-4

-- 10(66)
-s1s2-s3s2s1-s2s3-s2-s3-s3-s3-s3-s3
Alexander polynomial = 2t^6-7t^5+9t^4-9t^3+9t^2-7t+2

-- 10(67)
s1s2s3-s4s3-s2-s1s4-s3-s3-s2-s2s3-s2s4-s3
Alexander polynomial = -4t^4+14t^3-19t^2+14t-4

-- 10(68)
s1-s2s1-s2-s3-s3-s3-s3s2-s3-s2
Alexander polynomial = 2t^6-8t^5+12t^4-13t^3+12t^2-8t+2

-- 10(69)
s1-s2s3s4-s3s2-s3-s2-s1-s2-s4-s3-s3-s3-s2-s2
Alexander polynomial = 5t^4-14t^3+19t^2-14t+5

-- 10(70)
s1-s2-s3-s3-s3-s3-s3-s2-s2-s1-s2s3-s2
Alexander polynomial = -3t^6+8t^5-12t^4+13t^3-12t^2+8t-3

-- 10(71)
s1s2-s3s2-s1s3s3s3-s2s3-s2-s2-s2
Alexander polynomial = 2t^6-7t^5+13t^4-17t^3+13t^2-7t+2

-- 10(72)
-s1-s2-s3-s3-s4s3s2s1s3-s4s3s2-s4-s3s4-s3-s2-s4
Alexander polynomial = -4t^4+16t^3-23t^2+16t-4

-- 10(73)
s1s2-s3s2s2s2-s1s3-s2s3s3s3-s2
Alexander polynomial = 2t^6-7t^5+12t^4-15t^3+12t^2-7t+2

-- 10(74)
-s1s2-s3s4-s3-s2s1-s4-s5-s4s3s2s3-s4s3-s2s5-s4s3
Alexander polynomial = -2t^4+13t^3-23t^2+13t-2

-- 10(75)
s1s2-s3s2-s1s3s3s3-s2s3s3s3-s2
Alexander polynomial = 2t^6-7t^5+11t^4-13t^3+11t^2-7t+2

-- 10(76)
s1s2-s3s2-s1s3-s2-s2-s2s3s3s3-s2
Alexander polynomial = 2t^6-6t^5+10t^4-13t^3+10t^2-6t+2

-- 10(77)
-s1-s2-s3s2-s3s4s3-s2s1-s3s2-s3-s3-s3s2-s4
Alexander polynomial = -3t^4+9t^3-11t^2+9t-3

-- 10(78)
-s1-s2-s3s2-s3s4s3-s2s1-s3-s3-s3s2-s3s2-s4
Alexander polynomial = -3t^4+11t^3-15t^2+11t-3

-- 10(79)
-s1s2s2s3-s2s3s2-s4-s3s2s1-s2s3-s2-s3s4
Alexander polynomial = -4t^4+12t^3-15t^2+12t-4

-- 10(80)
s1-s2-s2-s2s3s4-s3s2-s3-s2-s1s2-s4-s3s2s3
Alexander polynomial = -4t^4+11t^3-13t^2+11t-4

-- 10(81)
-s1s2-s3-s3-s3-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = 2t^6-6t^5+7t^4-7t^3+7t^2-6t+2

-- 10(82)
s1-s2-s3-s4-s4-s3-s3-s2s3s4-s3-s2-s1-s2s3-s2
Alexander polynomial = 8t^4-26t^3+37t^2-26t+8

-- 10(83)
s1-s2s3s4s3-s2-s1-s2s3s3-s4s3-s2s3
Alexander polynomial = t^6-8t^5+22t^4-29t^3+22t^2-8t+1

-- 10(84)
-s1s2-s3s2s1s2-s3s4-s3s2-s3s4
Alexander polynomial = -t^6+7t^5-22t^4+33t^3-22t^2+7t-1

-- 10(85)
-s1-s1s2s3-s2s3s2-s1-s2s3s2-s1s2
Alexander polynomial = 2t^6-10t^5+23t^4-31t^3+23t^2-10t+2

-- 10(86)
-s1-s2s3s4-s3s4s3s2s2s1-s2-s3s4s3-s2s3
Alexander polynomial = -5t^4+22t^3-33t^2+22t-5

-- 10(87)
-s1s2s3-s2-s1s2s3-s2-s1s3s2-s1s2
Alexander polynomial = 2t^6-11t^5+24t^4-31t^3+24t^2-11t+2

-- 10(88)
-s1-s1s2-s1-s1s2-s1s2-s1s2
Alexander polynomial = -t^8+5t^7-12t^6+19t^5-21t^4+19t^3-12t^2+5t-1

-- 10(89)
s1-s2-s2s3-s2-s4s3-s2-s1-s2s3s4s3-s2
Alexander polynomial = t^6-8t^5+20t^4-25t^3+20t^2-8t+1

-- 10(90)
-s1s2-s3s2s1s2s3s4s4s4s3s3s2-s3-s4s3
Alexander polynomial = 7t^4-21t^3+29t^2-21t+7

-- 10(91)
-s1-s2s3s2s2s2-s1s2s2s3-s2s3s2
Alexander polynomial = 2t^6-9t^5+17t^4-21t^3+17t^2-9t+2

-- 10(92)
-s1-s1s2-s1-s2s3-s2-s2-s2-s1s2s3-s2
Alexander polynomial = 2t^6-9t^5+18t^4-23t^3+18t^2-9t+2

-- 10(93)
s1s2-s3s2-s3s2-s3s2-s1-s3-s2s3-s2
Alexander polynomial = 2t^6-10t^5+21t^4-27t^3+21t^2-10t+2

-- 10(94)
-s1-s1-s1s2-s1s2-s1s2-s1s2
Alexander polynomial = -t^8+5t^7-11t^6+17t^5-19t^4+17t^3-11t^2+5t-1

-- 10(95)
-s1s2-s3s2s1-s2s3-s2-s2s3s3-s2s3
Alexander polynomial = 2t^6-8t^5+17t^4-23t^3+17t^2-8t+2

-- 10(96)
s1s1s1-s2s1-s2s1s1-s2-s2
Alexander polynomial = -t^8+4t^7-9t^6+15t^5-17t^4+15t^3-9t^2+4t-1

-- 10(97)
s1-s2-s2s1s1-s2s1s1s1-s2
Alexander polynomial = -t^8+4t^7-9t^6+14t^5-15t^4+14t^3-9t^2+4t-1

-- 10(98)
-s1s2-s3s2s1-s2s3-s2s3s3-s2-s2s3
Alexander polynomial = 2t^6-8t^5+16t^4-21t^3+16t^2-8t+2

-- 10(99)
-s1s2-s1s2-s1-s1-s1-s1s2s2
Alexander polynomial = -t^8+4t^7-8t^6+12t^5-13t^4+12t^3-8t^2+4t-1

-- 10(100)
s1s1s1-s2s1s1s1-s2-s2-s2
Alexander polynomial = -t^8+3t^7-6t^6+10t^5-11t^4+10t^3-6t^2+3t-1

-- 10(101)
-s1s2-s1-s1-s1s2s2s2s2s2
Alexander polynomial = -t^8+3t^7-5t^6+7t^5-7t^4+7t^3-5t^2+3t-1

-- 10(102)
-s1-s2-s3s2-s3s4s3-s2s1-s3s2-s3s5s4s3-s2s3s2-s4-s5-s4
Alexander polynomial = 6t^2-13t+6

-- 10(103)
-s1s2s2-s3-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -2t^6+6t^5-10t^4+11t^3-10t^2+6t-2

-- 10(104)
s1-s2-s2s3s3-s2-s1s2-s4s3-s2s3s4-s3s2s3
Alexander polynomial = 3t^4-9t^3+13t^2-9t+3

-- 10(105)
s1s2s3s3s4-s3-s2-s1-s3-s3s2s3-s4s3-s2s4s4-s3
Alexander polynomial = 4t^4-13t^3+19t^2-13t+4

-- 10(106)
-s1s2-s3-s3s2s2s2s2s1-s2s3-s2-s3
Alexander polynomial = -2t^6+6t^5-9t^4+9t^3-9t^2+6t-2

-- 10(107)
s1s2-s3s2-s1s3-s2-s2-s2-s2s3-s2s3
Alexander polynomial = -2t^6+7t^5-11t^4+11t^3-11t^2+7t-2

-- 10(108)
s1-s2s3-s2-s2-s1s2-s4s3-s2s3s4-s3s2s3s3
Alexander polynomial = 3t^4-11t^3+17t^2-11t+3

-- 10(109)
-s1s2s2s2-s3s2s2s1-s2s3-s2-s3-s3
Alexander polynomial = -2t^6+7t^5-13t^4+15t^3-13t^2+7t-2

-- 10(110)
-s1s2s2-s3s2-s3s2s2s1-s2s3-s2-s3
Alexander polynomial = -2t^6+8t^5-14t^4+15t^3-14t^2+8t-2

-- 10(111)
s1s2-s3s2-s1s3-s2s3-s2-s2s3-s2-s2
Alexander polynomial = -2t^6+8t^5-15t^4+17t^3-15t^2+8t-2

-- 10(112)
-s1-s1-s1s2-s1-s1s2-s1-s1s2
Alexander polynomial = t^8-4t^7+9t^6-12t^5+13t^4-12t^3+9t^2-4t+1

-- 10(113)
-s1-s1-s1-s1s2-s1-s1s2-s1s2
Alexander polynomial = t^8-4t^7+8t^6-10t^5+11t^4-10t^3+8t^2-4t+1

-- 10(114)
-s1-s2s3s3-s4s3s2s1-s3-s3-s4s3s2-s3s4-s3-s2-s4
Alexander polynomial = 4t^4-14t^3+21t^2-14t+4

-- 10(115)
-s1-s1s2s2s2s2-s1s2s2s2
Alexander polynomial = t^8-3t^7+6t^6-8t^5+9t^4-8t^3+6t^2-3t+1

-- 10(116)
s1s1s1s1s1-s2s1s1-s2-s2
Alexander polynomial = t^8-3t^7+6t^6-7t^5+7t^4-7t^3+6t^2-3t+1

-- 10(117)
-s1s2-s1-s1s2s2s2s2s2s2
Alexander polynomial = t^8-3t^7+5t^6-5t^5+5t^4-5t^3+5t^2-3t+1

-- 10(118)
-s1s2s2s2-s3s2s2s2s1-s2s3-s2-s3
Alexander polynomial = 2t^6-5t^5+6t^4-7t^3+6t^2-5t+2

-- 10(119)
s1-s2s1-s2-s2-s2-s2-s2-s2-s2
Alexander polynomial = -t^8+3t^7-3t^6+3t^5-3t^4+3t^3-3t^2+3t-1

-- 10(120)
-s1s2-s3s4-s3-s2s1-s4-s5s4-s3s2-s4s3-s4s3-s2-s3s5-s4s3
Alexander polynomial = 4t^2-9t+4

-- 10(121)
s1s2-s3s2-s1s3-s2s3-s2-s2-s2-s2-s2
Alexander polynomial = 2t^6-5t^5+5t^4-5t^3+5t^2-5t+2

-- 10(122)
s1-s2-s2-s2s3-s2-s1s2-s4s3-s2s3s4-s3s2s3
Alexander polynomial = -3t^4+7t^3-7t^2+7t-3

-- 10(123)
-s1s2s2s2s2s2-s1s2s2s2
Alexander polynomial = -t^8+3t^7-4t^6+5t^5-5t^4+5t^3-4t^2+3t-1

```