Partial hyperclones on a finite set

The composition-closed sets of partial multi-valued operations, called partial hyperclones, defined on the finite set E(k)={0, 1, ..., k-1} (k⩾2) are investigated. It is shown that the lattice of all partial hyperclones is dually atomic and has only a finite number of dual atoms (maximal partial hyperclones). Some of them are presented in this paper. The full list of maximal restriction-closed partial hyperclones is obtained