From Bruhat intervals to intersection lattices and a conjecture of Postnikov

Axel Hultman; Svante Linusson; John Shareshian; Jonas Sjöstrand

From Bruhat intervals to intersection lattices and a conjecture of Postnikov

Axel Hultman
, Svante Linusson
, John Shareshian
, Jonas Sjöstrand

Research output: Contribution to conference › Paper › peer-review

Abstract

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.

Original language	English
Pages	203-214
Number of pages	12
State	Published - 2008
Event	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: Jun 23 2008 → Jun 27 2008

Conference

Conference	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
Country/Territory	Chile
City	Valparaiso
Period	06/23/08 → 06/27/08

Keywords

Bruhat order
Intersection lattices
Inversion arrangements

Cite this

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title = "From Bruhat intervals to intersection lattices and a conjecture of Postnikov",

abstract = "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.",

keywords = "Bruhat order, Intersection lattices, Inversion arrangements",

author = "Axel Hultman and Svante Linusson and John Shareshian and Jonas Sj{\"o}strand",

year = "2008",

language = "English",

pages = "203--214",

note = "20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 ; Conference date: 23-06-2008 Through 27-06-2008",

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TY - CONF

T1 - From Bruhat intervals to intersection lattices and a conjecture of Postnikov

AU - Hultman, Axel

AU - Linusson, Svante

AU - Shareshian, John

AU - Sjöstrand, Jonas

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Bruhat order

KW - Intersection lattices

KW - Inversion arrangements

UR - https://www.scopus.com/pages/publications/84860477260

M3 - Paper

AN - SCOPUS:84860477260

SP - 203

EP - 214

T2 - 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08

Y2 - 23 June 2008 through 27 June 2008

ER -

From Bruhat intervals to intersection lattices and a conjecture of Postnikov

Abstract

Conference

Keywords

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Cite this