Essential arities of term operations in finite algebras Original Research Article

Given an algebra A, pn(A) denotes the number of distinct n-ary term operations t:An → A of A which depend on all n variables. We solve some problems of Berman, Grätzer and Kisielewicz concerning the sequence 〈p0(A), p1(A),…, pn(A),…〉 in case ¦A¦ is finite. Our methods yield new results about totally symmetric functions on a finite set.