Author

D. Poliakova

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Preprint Aug 2026

Order dimension beyond rank for simplicial hyperplane arrangements

We show that the order dimension of the poset of regions in a simplicial hyperplane arrangement can exceed its rank, answering a question of Reading and Segovia. Examples are Coxeter arrangements \(H_4\) and \(E_6\), with \( \dim W(H_4) \geq 5\) and \( \dim W(E_6) \geq 7\).

D. Poliakova · 0 citations