Semirigid sets of central relations over a finite domain

A set of central h-ary relations on a set A is called semirigid if the clones of k-valued logic functions determined by the relations share only the clone K_h-1 consisting of all projections and all functions assuming at most h-1 values (1<h<k:=| A|>2; K₁ is the set of trivial functions, i.e., the clone consisting of all constants and all projections). The problem of determining semirigid sets of central relations is studied. For the set of h-ary central relations with the centers of the largest size, it is shown that the set consisting of all such relations is the only semirigid set. It is also shown that the minimum size of a semirigid set of central h-ary relations is h+1. For k=4, semirigid sets of binary central relations are investigated in detail