Virtual Knot 4.29
- 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-O3-O4-U3-U2-U4-
- PD presentation
- PD[X[2,8,3,1], X[6,1,7,2], X[5,3,6,4], X[7,4,8,5]]
- Jones polynomial
- - q-4 - q-7/2 + q-3 + q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.9, 4.15, 4.37, 4.48, 4.61, 4.69, 4.78
- Cabled Jones polynomials
- q-25/2 + q-23/2 + 2q-21/2 - 3q-19/2 - 2q-17/2 - q-15/2 + 2q-13/2 + q-11/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- - q-25 + 3q-24 - 4q-45/2 - 4q-22 - 15q-43/2 - 34q-21 - 59q-41/2 - 89q-20 - 109q-39/2 - 138q-19 - 114q-37/2 - 102q-18 - 12q-35/2 + 46q-17 + 142q-33/2 + 212q-16 + 222q-31/2 + 268q-15 + 193q-29/2 + 175q-14 + 56q-27/2 + q-13 - 50q-25/2 - 106q-12 - 107q-23/2 - 126q-11 - 84q-21/2 - 70q-10 - 44q-19/2 - 29q-9 - 14q-17/2 - 5q-8 - q-15/2 + q-5 - 2q-4 - 2q-7/2 + 2q-3 + 2q-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-2 + 2s-1) t-3 + (s-4 - s-3 + s-2 - 1) t-2 + (- s-3 + 2s-2 - s-1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2