 \(\mathbb{N} =\{0,1,2,\ldots\}\) denotes the set of natural numbers, \(\mathbb{N}^k\) denotes the cross product \(\mathbb{N} \times \ldots \times \mathbb{N}\) \(k\)-times, and \(\vec{n}\) denotes a vector of fixed numbers \(n_0,\ldots,n_{k-1}\) (when the arity is clear from context).