Virtual Knot 4.1
- This virtual knot is not equivalent to its vertical mirror image.
- This virtual knot is not equivalent to its horizontal mirror image.
- The two mirror images are not equivalent to each other.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2-U1-U2-O3-O4-U3-U4-
- PD presentation
- PD[X[2,8,3,1], X[3,1,4,2], X[6,4,7,5], X[7,5,8,6]]
- Jones polynomial
- q-5 - 2q-4 - 2q-7/2 + q-3 + 2q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.3, 4.7, 4.53, 4.73
- Cabled Jones polynomials
- - q-29/2 + 2q-27/2 + 2q-25/2 - 3q-23/2 - 4q-21/2 - 2q-19/2 + 7q-17/2 + 4q-15/2 - 3q-11/2 - 3q-9/2 - q-5/2 + q-3/2 - q-1/2
- q-28 - 2q-27 + 2q-26 - 2q-25 - 6q-49/2 - 3q-24 + 4q-47/2 + 6q-23 + 8q-45/2 + 2q-22 + 2q-43/2 + 13q-21 + 4q-41/2 + 7q-20 + 16q-39/2 + 18q-19 + 12q-37/2 - 46q-18 - 108q-35/2 - 143q-17 - 172q-33/2 - 139q-16 - 92q-31/2 + 13q-15 + 152q-29/2 + 216q-14 + 260q-27/2 + 215q-13 + 164q-25/2 + 90q-12 - 16q-23/2 - 68q-11 - 108q-21/2 - 94q-10 - 82q-19/2 - 67q-9 - 34q-17/2 - 18q-8 - 4q-15/2 - 2q-7 + 2q-6 + 3q-5 - 4q-4 - 4q-7/2 + 2q-3 + 4q-5/2 + 2q-2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + 2s-3 - s-2) t-4 + (2s-4 - 2s-3 - 2s-2 + 2s-1) t-3 + (- s-4 - 2s-3 + 4s-2 - 1) t-2 + (2s-3 - 2s-1) t-1 + (- s-2 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -4