Axel Hultman ; Svante Linusson ; John Shareshian ; Jonas Sjöstrand
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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)
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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
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Axel Hultman;Svante Linusson;John Shareshian;Jonas Sjöstrand
1 Department of Mathematics [Sweden]
2 Department of Mathematics
3 Department of Mathematics and Physics
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w∈Sn 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.
Enumerative, Algebraic and Topological Combinatorics; Funder: National Science Foundation; Code: 0604233
Bibliographic References
6 Documents citing this article
Hiraku Abe;Sara Billey, Project Euclid (Cornell University), Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry, pp. 1-52, 2018, Osaka City University, 10.2969/aspm/07110001, https://projecteuclid.org/euclid.aspm/1538622994.
Aaron J. Klein;Joel Brewster Lewis;Alejandro H. Morales, 2013, Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams, Journal of Algebraic Combinatorics, 39, 2, pp. 429-456, 10.1007/s10801-013-0453-x, https://doi.org/10.1007/s10801-013-0453-x.