Virtual Knot 3.4
- 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 equivalent to each other.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2+U1-U3-U2+O3-
- PD presentation
- PD[X[2,6,3,1], X[4,2,5,1], X[3,5,4,6]]
- Jones polynomial
- q-2 - q-1 - q-1/2 + 1 + q1/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 3.2, 4.27, 4.81, 4.84, 4.88, 4.104
- Cabled Jones polynomials
- - q-13/2 + 2q-11/2 + 2q-9/2 - q-7/2 - 4q-5/2 - 2q-3/2 + 2q-1/2 + q1/2 - q5/2
- q-13 - 2q-12 + 2q-11 - 2q-10 - 6q-19/2 - 3q-9 + 4q-17/2 + 8q-8 + 21q-15/2 + 17q-7 + 22q-13/2 + 22q-6 - 3q-11/2 - 12q-5 - 42q-9/2 - 37q-4 - 33q-7/2 - 30q-3 - 3q-5/2 + 4q-2 + 24q-3/2 + 23q-1 + 13q-1/2 + 13 + 3q1/2 + 2q1 - q3/2 - 4q2 + 2q3 + 2q7/2 - 2q9/2 + q11/2
- - q-43/2 + 2q-41/2 - 2q-39/2 + 2q-37/2 + 6q-35/2 - 3q-33/2 - 2q-29/2 + 79q-27/2 + 195q-25/2 + 302q-23/2 + 315q-21/2 + 118q-19/2 - 181q-17/2 - 494q-15/2 - 614q-13/2 - 480q-11/2 - 209q-9/2 + 88q-7/2 + 244q-5/2 + 282q-3/2 + 214q-1/2 + 106q1/2 + 33q3/2 - 9q5/2 + q7/2 - q9/2 + 2q11/2 - 2q15/2 + 2q17/2 - q19/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (s-2 - s-1) t-1 + (- s-2 + 1) + (s-1 - 1) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 2.1, 3.2, 4.18, 4.20, 4.27, 4.33, 4.34, 4.38, 4.40, 4.44, 4.49, 4.52, 4.60, 4.88, 4.94
- Self linking number
- -2