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

Abstract : 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 $h$.
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Alexander Woo. Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.893-902, ⟨10.46298/dmtcs.2705⟩. ⟨hal-01185397⟩

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