Virtual Knot 4.32
- 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[5,4,6,3], X[7,5,8,4]]
- Jones polynomial
- - q-3/2 - q-1 + q-1/2 + 3 + q1/2 - q1 - q3/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.2, 4.6, 4.8, 4.12, 4.17, 4.51, 4.58, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-9/2 + 2q-7/2 + 4q-5/2 - 2q-3/2 - 7q-1/2 - 5q1/2 + q3/2 + 5q5/2 + q7/2 - q11/2
- - q-23/2 + 3q-21/2 - 3q-19/2 - 2q-9 + 6q-8 + 2q-15/2 - 4q-7 - 2q-13/2 - 27q-6 - 38q-11/2 - 76q-5 - 92q-9/2 - 64q-4 - 49q-7/2 + 38q-3 + 80q-5/2 + 154q-2 + 205q-3/2 + 172q-1 + 152q-1/2 + 38 - 36q1/2 - 109q1 - 173q3/2 - 141q2 - 129q5/2 - 55q3 - 4q7/2 + 23q4 + 55q9/2 + 36q5 + 37q11/2 + 18q6 + 2q13/2 - 8q15/2 - q8 - 2q17/2 - 2q9 + 2q21/2 - q23/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-2 + 1) t-1 + (s-2 + s-1 - 1 - s) + (- s-1 + s) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 3.1, 4.10, 4.17, 4.19, 4.23, 4.35, 4.42, 4.50, 4.57, 4.67, 4.70, 4.79
- Self linking number
- 0