Minimal Coverings of Maximal Partial Clones

A partial function f on a k-element set E_k is a partial Sheffer function if every partial function on E_k is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on E_k, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on E_k. We show that for each k ges3 there exists a unique minimal covering.