Skip to Main content Skip to Navigation
Conference papers

From Bruhat intervals to intersection lattices and a conjecture of Postnikov

Abstract : We prove the conjecture of A. Postnikov that ($\mathrm{A}$) the number of regions in the inversion hyperplane arrangement associated with a permutation $w \in \mathfrak{S}_n$ is at most the number of elements below $w$ in the Bruhat order, and ($\mathrm{B}$) that equality holds if and only if $w$ avoids the patterns $4231$, $35142$, $42513$ and $351624$. Furthermore, assertion ($\mathrm{A}$) is extended to all finite reflection groups.
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185184
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Wednesday, August 19, 2015 - 11:44:45 AM
Last modification on : Thursday, February 24, 2022 - 1:38:03 PM
Long-term archiving on: : Friday, November 20, 2015 - 10:43:04 AM

File

dmAJ0118.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Axel Hultman, Svante Linusson, John Shareshian, Jonas Sjöstrand. From Bruhat intervals to intersection lattices and a conjecture of Postnikov. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.203-214, ⟨10.46298/dmtcs.3648⟩. ⟨hal-01185184⟩

Share

Metrics

Record views

37

Files downloads

351