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$Conference paper

Authors: Alexander Woo ORCID1,2

  • 1 Department of Mathematics, St. Olaf College, Northfield
  • 2 Department of Mathematics [Northfield, St. Olaf College]

[en]
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 $h$.

[fr]
On démontre la conjecture de Billey et Braden sur les permutations w pour lesquelles le polynôme de Kazhdan-Lusztig $P_id,w(q)=1+q^h$ pour un entier $h$. On emploie une résolution des singularités présentées par Cortez et une méthode de Polo pour calculer ces polynômes.

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: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Kazhdan-Lusztig polynomials, Schubert varieties
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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