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A virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For an even virtual link diagram, we define a certain linking invariant which is similar to the linking number. In contrast to the usual linking number, our linking invariant is not preserved under the forbidden moves. In particular, for two fused isotopic even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.

The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e. curves with the same combinatorics and different embedding in $ℂ{\mathbb{P}}^2$. Differentiating Shimada's ${\pi }_1$-equivalent Zariski pair by the linking set, we prove, in the present paper, that this invariant is not determined by the fundamental group of the curve.

A parity is a rule to assign labels to the crossings of knot diagrams in a way compatible with the Reidemeister moves. Parity functors can be viewed as parities which provide to each knot diagram its own coefficient group that contains parities of the crossings. In the paper we describe the universal oriented parity functors for free knots and for knots in a fixed surface.