Virtual Knot 4.22
- 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+U2-U3+U4+
- PD presentation
- PD[X[2,8,3,1], X[5,1,6,2], X[6,4,7,3], X[7,5,8,4]]
- Jones polynomial
- - q-3/2 + q-1/2 + 2 - q1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.14, 4.20, 4.34, 4.40, 4.52, 4.60, 4.64
- Cabled Jones polynomials
- - q-11/2 + 2q-9/2 + 3q-7/2 + 2q-5/2 - 3q-3/2 - 7q-1/2 - 3q1/2 + q3/2 + 3q5/2 + q7/2
- - q-23/2 + 2q-21/2 - 2q-19/2 + 2q-17/2 + 7q-8 + 3q-15/2 - 4q-7 - 7q-13/2 - 27q-6 - 26q-11/2 - 56q-5 - 61q-9/2 - 73q-4 - 66q-7/2 - 45q-3 - 27q-5/2 + 19q-2 + 59q-3/2 + 121q-1 + 141q-1/2 + 159 + 121q1/2 + 100q1 + 43q3/2 + q2 - 43q5/2 - 68q3 - 64q7/2 - 69q4 - 52q9/2 - 47q5 - 20q11/2 - 14q6 - 5q13/2 - 3q7 + 3q15/2 + 3q8
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-1 + (- s-2 + s-1 + 1 - s) + (s-2 + s-1 - 2) t + (- s-1 + s) t2
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.14, 4.39, 4.84
- Self linking number
- -2