The $r$-matching sequencibility of complete multi-$k$-partite $k$-graphs

Alspach [{\sl Bull. Inst. Combin. Appl.}~{\bf 52} (2008), 7–20] defined the maximal matching sequencibility of a graph $G$, denoted~$ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$ consecutive edges form a matching. In this paper, we consider the natural analogue for hypergraphs of this and related results and determine $ms(\lambda {\mathcal{K}}_{n_1,\dots ,n_k})$ where $\lambda {\mathcal{K}}_{n_1,\dots ,n_k}$ denotes the multi-$k$-partite $k$-graph with edge multiplicity $\lambda$ and parts of sizes $n_1,\dots ,n_k$, respectively. It turns out that these invariants may be given surprisingly precise and somewhat elegant descriptions, in a much more general setting.