In a hypergraph, we have vertices $V$ and hyperedges $H$, where each hyperedge is a subset of $V$. Suppose that we would like the hyperedges to be (ordered) tuples, rather than subsets. Does this variant of a hypergraph have a name? I found the definition of a directed hypergraph (http://www.cis.upenn.edu/~lhuang3/wpe2/papers/gallo92directed.pdf) but that doesn't appear to be it.
Thank you.
This isn't exactly what you are looking for but it is similar.
Frankl defines an $\textbf{oriented k-uniform hypergraph}$ as an pair of vertices and edges, where each edge is a $k$-tuple of distinct vertices with the following extra condition: for any subset of size $k$, at most 1 of the possible $k!$ edges consisting of these vertices is actually present. For example, an oriented graph is a digraph without any pair of arcs $\vec{ij}$ and $\vec{ji}$. There has been recent research on complete oriented $k$-uniform hypergraphs, which are called $\textit{hypertournaments}$.