Decomposition of k-ary relations (Q751668)

A decomposition theory due to \textit{W. Cunningham} and \textit{J. Edmonds} [Can. J. Math. 32, 734-765 (1980; Zbl 0442.05054)] is applied to k-ary relations, \(k\geq 3\). The case \(k=2\), i.e. decomposition of directed graphs is dealt with in \textit{W. Cunningham} [SIAM J. Algebraic and Discrete Methods 3, 214-228 (1982; Zbl 0497.05031)]. It is proved that there is a unique minimal decomposition of a k-ary relation into smaller ones which are either indecomposable or ``highly'' decomposable.