Alexander Woo - Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$

dmtcs:2705 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2705
Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$

Authors: Alexander Woo ORCID-iD1

  • 1 Department of Mathematics, St. Olaf College, Northfield

Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial$ P_id,w(q)=1+q^h$ for some $h$.

https://doi.org/10.46298/dmtcs.2705
Source: HAL:hal-01185397v1
Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Kazhdan-Lusztig polynomials,Schubert varieties,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Vertical Integration of Research and Education in the Mathematical Sciences - VIGRE: Research Focus Groups in Mathematics; Funder: National Science Foundation; Code: 0135345

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Source : ScholeXplorer IsRelatedTo DOI 10.1090/s0894-0347-98-00249-5
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Lattice paths and Kazhdan-Lusztig polynomials

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