Universal Polynomials of Several Variables for Classes of Linear Functions

Abstract

It was shown earlier that product \(xy\) for \(k=6l\pm 1\) is a universalfunction in the class of linear functions of two variables, and there exist no universal polynomials for even \(k\) in classes of linear functions of two variables. This work proves that polynomial \(xy+xz+yz\) is universal for classes of linear functions of three variables for arbitrary odd \(k\) and polynomial \(xy+zw\) is universal for classes of linear functions of four variables for arbitrary \(k\).