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Let be the superspace ring of polynomial-valued differential forms on affine n-space. The natural action of the symmetric group Sₙ on n-space induces an action of Sₙ on. The superspace coinvariant ring is the quotient SR of by the ideal generated by Sₙ-invariants with vanishing constant term. We give the first explicit basis of SR, proving a conjecture of Sagan and Swanson. Our techniques use the theory of hyperplane arrangements. We relate SR to instances of the Solomon-Terao algebras of Abe-Maeno-Murai-Numata and use exact sequences relating the derivation modules of certain `southwest closed' arrangements to obtain the desired basis of SR.
Angarone et al. (Sat,) studied this question.