Geodesic
On Bruhat posets associated to compositions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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The purpose of this work is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes. 
@article{DMTCS_2014_special_265_a35,
     author = {Can, Mahir Bilen and Cherniavsky, Yonah},
     title = {On {Bruhat} posets associated to compositions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2410},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2410/}
}
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Can, Mahir Bilen; Cherniavsky, Yonah. On Bruhat posets associated to compositions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2410. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2410/

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