Representations of hypergroups by generalized permutations (Q1193497)

For a given set \(X\) let \(M_ X\) be the set of all generalized permutations of \(X\), i.e., all mappings \(f: X\to {\mathcal P}(X)\) with \(\bigcup_{x\in X}f(x) = X\). Then \(M_ X\) carries a canonical universal hypergroup structure. In this paper, certain subhypergroups of \(M_ X\) are studied. Moreover, representations of a given hypergroup \(X\) on \(M_ X\) are investigated.