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From Bruhat intervals to intersection lattices and a conjecture of Postnikov
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-6339-2230
2008 (English)In: FPSAC - Int. Conf. Form. Power Ser. Algebraic Comb., 2008, 203-214 p.Conference paper, Published paper (Refereed)
Abstract [en]

We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ S n is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups.

Place, publisher, year, edition, pages
2008. 203-214 p.
Series
FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics
Keyword [en]
Bruhat order, Intersection lattices, Inversion arrangements, Hyperplane arrangements, Reflection group, Combinatorial circuits, Combinatorial mathematics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-153340Scopus ID: 2-s2.0-84860477260OAI: oai:DiVA.org:kth-153340DiVA: diva2:755215
Conference
20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, 23 June 2008 through 27 June 2008, Valparaiso, Chile
Note

QC 20141014

Available from: 2014-10-14 Created: 2014-10-03 Last updated: 2014-10-14Bibliographically approved

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Linusson, Svante

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  • nn-NB
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  • Other locale
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Output format
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