Some results on homogeneous symmetric polynomial-like Boolean functions

Abstract. Polynomial-like Boolean functions form a class of the Boolean functions invariant with respect to a special transform of the linear space of the two-valued logical functions. Another special set of the Boolean-functions are the set of the symmetric functions. In earlier articles we introduced the class of the symmetric polynomial-like Boolean functions, investigated some elementary properties of such functions and dealt with the special case of the homogeneous symmetric polynomial-like Boolean functions. One of our results determined the integers \(n\) for a given nonnegatíve integer \(k\) so that the Boolean function belonging to \(p^{(n;k)}\) is polynomial-like. Now we continue the investigation of the homogeneous symmetric polynomial-like Boolean functions, and among others we deal with the reverse problem, that is, we determine the number of the homogeneous symmetric, \(n\)-indeterminate polynomials for which the Boolean functions are polynomial-like.