On universal polynomials depending on few variables for classes of linear functions

Recieved: 06/06/2023

Accepted: 06/30/2023

Published: 11/28/2023

Keywords: generation, universal function, sum modulo, polynimial

To cite this article

Voronenko A.A. On universal polynomials depending on few variables for classes of linear functions. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 4, p.17-20 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–4–17–20.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Voronenko A.A. (Lomonosov Moscow State University (MSU))

Abstract

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l ± 1. Also it was shown that there is no universal polynomials for the class of linear functions depending on two arguments for any even k. In this paper we prove that polynomial xy + xz + yz is universal for classes of linear functions depending on three arguments for arbitrary odd k and polynomial xy + zw is universal for classes of linear functions depending on four arguments for any k.