Uniqueness of minimal coverings of maximal partial clones

A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f . Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minimal covering.