Geodesic
Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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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 $h$. 
@article{DMTCS_2009_special_256_a27,
     author = {Woo, Alexander},
     title = {Permutations with {Kazhdan-Lusztig} polynomial $ P_id,w(q)=1+q^h$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2705},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2705/}
}
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%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
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Woo, Alexander. Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2705. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2705/

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