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From Bruhat interva...
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
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- Hultman, Axel (författare)
- KTH,Matematik (Avd.)
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- Linusson, Svante (författare)
- KTH,Matematik (Avd.)
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- Shareshian, John (författare)
- Washington University
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- Sjöstrand, Jonas, 1981- (författare)
- Stockholms universitet,Mälardalens högskola,Akademin för utbildning, kultur och kommunikation,CEK,Centrum för evolutionär kulturforskning
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KTH Matematik (Avd) (creator_code:org_t)
- Elsevier BV, 2009
- 2009
- Engelska.
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Ingår i: Journal of combinatorial theory. Series A (Print). - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 116:3, s. 564-580
- Relaterad länk:
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Bruhat order
- Inversion arrangements
- Pattern avoidance
- smooth schubert varieties
- arrangements
- Mathematics/Applied Mathematics
- MATHEMATICS
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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