Bruhat order, smooth Schubert varieties, and hyperplane arrangements

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dc.creatorOh, Suho
dc.creatorPostnikov, Alexander
dc.creatorYoo, Hwanchul
dc.date2007-09-20
dc.date.accessioned2026-07-07T08:31:07Z
dc.date.available2026-07-07T08:31:07Z
dc.descriptionThe aim of this article is to link Schubert varieties in the flag manifold with hyperplane arrangements. For a permutation, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincare polynomial of the corresponding Schubert variety if and only if the Schubert variety is smooth. We give an explicit combinatorial formula for the Poincare polynomial. Our main technical tools are chordal graphs and perfect elimination orderings.
dc.description14 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0709.3259
dc.identifierhttp://arxiv.org/abs/0709.3259
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138420
dc.subjectCombinatorics
dc.titleBruhat order, smooth Schubert varieties, and hyperplane arrangements
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