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On Bruhat posets associated to compositions

Abstract : 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.
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https://hal.inria.fr/hal-01207600
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Mahir Bilen Can, Yonah Cherniavsky. On Bruhat posets associated to compositions. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.405-416, ⟨10.46298/dmtcs.2410⟩. ⟨hal-01207600⟩

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