Axel Hultman ; Svante Linusson ; John Shareshian ; Jonas Sjöstrand - From Bruhat intervals to intersection lattices and a conjecture of Postnikov

dmtcs:3648 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3648
From Bruhat intervals to intersection lattices and a conjecture of PostnikovConference paper

Authors: Axel Hultman 1; Svante Linusson 1; John Shareshian 2; Jonas Sjöstrand 3

  • 1 Department of Mathematics [Sweden]
  • 2 Department of Mathematics
  • 3 Department of Mathematics and Physics

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.

https://doi.org/10.46298/dmtcs.3648
Source: HAL:hal-01185184v1
Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Bruhat order,inversion arrangements,intersection lattices,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Enumerative, Algebraic and Topological Combinatorics; Funder: National Science Foundation; Code: 0604233

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