Acta Mathematica Vietnamica
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HERBIE: A CUBIC LINEAR COUNTEREXAMPLE TO THE DEPENDENCE PROBLEM
MICHIEL DE BONDT
Abstract
We show that there exists a cubic linear counterexample to the (Homogeneous) Dependence Problem in dimension 53. More generally, there exists a power linear counterexample of degree $d$ to the (H)DP (in sufficiently large dimensions), if and only if there exists any counterexample of degree $d$ to the (H)DP.