A Gorni-Zampieri Pair of a Homogeneous Polynomial Map

Abstract

In this paper, we improve the algorithm and rewrite the function make-Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP (dependence problem for power linear maps) are obtained, including one in the lowest dimension ($n = 48$) in all such counterexamples one has found up to now.