Year: 2026
Type: preprint
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 \( \dim W(E_6) \geq 7\).
Source: arXiv (Cornell University)
Author: Poliakova, Daria
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G813609259
OpenAlex ID: W7203616728
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