On Bruhat posets associated to compositions ∗

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. Résumé. Le but de ce travail est de lancer une tude combinatoire de l’ordre de Bruhat-Chevalley sur certains ensembles de permutations obtenues en omettant les parenthses de leur notation cyclique standard. En particulier, nous montrons que ces ensembles forment born, class, unimodale, rang-symtrique et posets EL-shellable. De plus, nous dterminons les types de complexes d’ordre associs d’homotopie.