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From Bruhat intervals to intersection lattices and a conjecture of Postnikov
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- Hultman, Axel (author)
- KTH,Matematik (Avd.)
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- Linusson, Svante (author)
- KTH,Matematik (Avd.)
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- Shareshian, John (author)
- Washington University
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- KTH Matematik (Avd) (creator_code:org_t)
- Elsevier BV, 2009
- 2009
- English.
- In: Journal of combinatorial theory. Series A (Print). - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 116:3, s. 564-580
- Journal article (peer-reviewed)
Abstract
Subject headings
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- We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w is an element of (sic)(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. A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns.
Subject headings
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Bruhat order
- Inversion arrangements
- Pattern avoidance
- smooth schubert varieties
- arrangements
- Mathematics/Applied Mathematics
- MATHEMATICS
Publication and Content Type
- ref (subject category)
- art (subject category)
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