From Bruhat intervals to intersection lattices and a conjecture of Postnikov
2008 (English)In: FPSAC - Int. Conf. Form. Power Ser. Algebraic Comb., 2008, 203-214 p.Conference paper (Refereed)
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.
, FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics
Bruhat order, Intersection lattices, Inversion arrangements, Hyperplane arrangements, Reflection group, Combinatorial circuits, Combinatorial mathematics
IdentifiersURN: urn:nbn:se:kth:diva-153340ScopusID: 2-s2.0-84860477260OAI: oai:DiVA.org:kth-153340DiVA: diva2:755215
20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, 23 June 2008 through 27 June 2008, Valparaiso, Chile
QC 201410142014-10-142014-10-032014-10-14Bibliographically approved