Tutorial

Let us first set the generic notation and definitions common to all the semilattices inheriting from CoordinateSemilattice. Additional notations and definitions will be introduced as needed for the particular semilattices presented.

The tuple \(\mathcal{S}=(\mathcal{V}, \mathcal{E})\) is a coordinate semilattice of dimension \(d\) if

• \(\mathcal{S}\) is connected
• there exist a unique vertex \(r\in\mathcal{V}\), denoted root, such that \(r.\text{parents} = \varnothing\)
• each vertex \(v\in\mathcal{V}\) has at most \(d\) children
• each vertex \(v\in\mathcal{V}\) which is \(v.\text{level}\) edges away from the root has at most \(\min(d, v.\text{level})\) parents (the connectivity properties implies that any vertex but the root must have at least one parent and up to d parents).