The paper gives a bijective proof of Zaslavsky's level enumeration for hyperplane arrangements via centralization, shows that the counts depend only on the intersection poset, and derives a general characteristic polynomial for geometric semilattices with applications to braid deformations.
On geometric semilattices
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Region level via centralization for hyperplane arrangements and beyond
The paper gives a bijective proof of Zaslavsky's level enumeration for hyperplane arrangements via centralization, shows that the counts depend only on the intersection poset, and derives a general characteristic polynomial for geometric semilattices with applications to braid deformations.