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LIT-355: An Introduction to Hyperplane Arrangements

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Properties5
StatusActive — read in full 2026-09-29 (NOTE-313); worth reading as the standard open introduction to real hyperplane arrangements. It is the best reachable source for "regions", the intersection poset and Zaslavsky's region-count theorem, with complete proofs of the region formula. Read it knowing that it never uses the oriented-matroid vocabulary of "topes" or "covectors" (it cites Björner et al., *Oriented Matroids*, only in passing) and that it does not cite Zaslavsky's own texts.
Version2
Tagsmathematics
Cited as “paper” byNOTE-313 — An Introduction to Hyperplane Arrangements
Cited as “source” byTHEORY-430 — A real hyperplane arrangement in ℝⁿ has (−1)ⁿχ(−1) regions and (−1)^rank χ(1) bounded regions, where χ is the characteristic polynomial of its intersection poset, so these counts depend only on which hyperplanes meet and in what dimension, not on the shapes of the regions

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Stanley (2006), Lecture notes from the IAS/Park City Mathematics Institute lecture series, 12–19 July 2004 (author’s version of 26 February 2006, linked from the author’s page); printed in Geometric Combinatorics (E. Miller, V. Reiner, B. Sturmfels, eds.), IAS/Park City Mathematics Series 13, American Mathematical Society, 2007, pp. 389–496 (Crossref-verified DOI and pages); author’s errata of 18 October 2020 — DOI-10.1090/pcms/013/08

Standing in the record

Filed on 2026-09-29 as a supplemental reading. The close readings of the owner’s prior-art novelty map’s references found the map’s citation for this point wrong, or its source unreachable, and this work is the candidate replacement. published: is the first appearance (ADR-002).

It was filed Deferred, unread. NOTE-313 is the close reading of 2026-09-29, and it placed the work: Active — worth reading as the standard open introduction to real hyperplane arrangements. It is the best reachable source for “regions”, the intersection poset and Zaslavsky’s region-count theorem, with complete proofs of the region formula. Read it knowing that it never uses the oriented-matroid vocabulary of “topes” or “covectors” (it cites Björner et al., Oriented Matroids, only in passing) and that it does not cite Zaslavsky’s own texts.

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