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arXiv · 2608.14092

Order dimension beyond rank for simplicial hyperplane arrangements

Daria Poliakova
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Abstract

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 \( \dim W(E_6) \geq 7\).

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Daria Poliakova. 2026-08-14. Order dimension beyond rank for simplicial hyperplane arrangements. https://arxiv.org/abs/2608.14092

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