• 1 Department of Mathematics [Tulane, New Orleans]
• 2 Department of Computer Science and Mathematics [Ariel university]

[en]
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.

[fr]
Le but de ce travail est de lancer une étude combinatoire de l’ordre de Bruhat-Chevalley sur certains ensembles de permutations obtenues en omettant les parenthèses de leur notation cyclique standard. En particulier, nous montrons que ces ensembles forment des posets bornés, classés, unimodaux, rang-symétriques et EL-shellable. De plus, nous déterminons les types de complexes d’ordre associés d’homotopie.