Overcrossing handedness

There are two chiralities of trefoil knots right-handed and left-handed, depending on overcrossing handedness along the oriented curve (see Figure 6). These two knots are not distinguished by the polynomial A(t). For complicated knots, the computation of the entire polynomial is feasible, but it can be a formidable task. i... 

One can design other shape descriptors that preserve the original geometric information while taking into account the handedness. For example, the handedness can be included in a colored overcrossing graph. 1 ... 

Similarly, we can extend the notion of overcrossing probabilities to include handedness. Consider a given 2D projection of the oriented polymer... 

Figure 6 Examples of simplest knots in molecular loops. The trefoil knot exhibits chirality. The handedness is determined by the right-hand rule. All three overcrossings in the (T+) knot have handedness of +1, whereas this is —1 in the case of the (T ) knot.

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