Deformations of Coxeter hyperplane arrangements

DOI10.1006/jcta.2000.3106zbMath0962.05004arXivmath/9712213OpenAlexW2101769805MaRDI QIDQ1584672

Alexander Postnikov, Richard P. Stanley

Publication date: 13 June 2001

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9712213

zbMATH Keywords

characteristic polynomialhyperplane arrangementsShi arrangementCoxeter arrangementCatalan arrangementalternating treesgeneric arrangementenumeration problem of regionsLinial arrangementtruncated affine arrangements

Mathematics Subject Classification ID

Trees (05C05) Exact enumeration problems, generating functions (05A15) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Asymptotic enumeration (05A16)

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Cites Work

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• The Kazhdan-Lusztig cells in certain affine Weyl groups
• On geometric semilattices
• Combinatorics and topology of complements of hyperplanes
• Intransitive trees
• On a family of hyperplane arrangements related to the affine Weyl groups
• The cohomology ring of the colored braid group
• Free arrangements and rhombic tilings
• Extended linial hyperplane arrangements for root systems and a conjecture of Postnikov and Stanley
• Characteristic polynomials of subspace arrangements and finite fields
• On the Enumeration of Decision Patterns Involving $n$ Means
• Foundational aspects of theories of measurement
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• Sign Types Corresponding to an Affine Weyl Group
• Hyperplane arrangements, interval orders, and trees.