The dijoin conjecture for oriented graphs

Let $L$) and $R$ be oriented graphs. Their dijoin $L\rightarrow R$ is formed from vertex-disjoint copies of $L$ and $R$, with every edge directed from $L$ to $R$.

Dijoin conjecture.

$$\operatorname{inv}(L\rightarrow R)=\operatorname{inv}(L)+\operatorname{inv}(R).$$

This conjecture is refuted in the paper by a counterexample, although it holds in several special cases.