Minimal partial clones
Ferdinand Börner, Lucien Haddad, Reinhard Pöschel · Bulletin of the Australian Mathematical Society · 1991
LetAbe a finite set. A partial clone on A is a composition closed set of operations containing all projections. It is well known that the partial clones on A, ordered by inclusion, form a lattice. We show that the minimal partial clones onAare: (a) minimal clones of full operations or (b) generated by partial projections defined on a totally reflexive and totally symmetric domain.