Two counterexamples for power ideals of arrangements

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We disprove Holtz and Ron's conjecture that the power ideal Cₐ,₋₂ of a hyperplane arrangement A (also called the "internal zonotopal space") is generated by A-monomials. We also show that, in contrast with the case k ≥ -2, the Hilbert series of Cₐ,ₖ is not determined by the matroid of A for k ≤ -6.