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. ...

Abstract An h -tiling on a finite simplicial complex is partition of its geometric realization by maximal simplices deprived several codimension one faces together with possibly their remaining face highest codimension. In this last case, the tiles are said to be critical. thus induces partitioning poset closed or semi-open intervals. We prove existence -tilings every after finitely many stella...

The antiprism triangulation provides a natural way to subdivide simplicial complex \(\Delta \), similar barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the of chains multi-pointed faces from point view, by successively applying construction, or balanced stellar subdivisions, on geometric view. This paper studie...

We generalize results of Calderbank, Hanlon and Robinson on the representation of the symmetric group on the homology of posets of partitions with restricted block size. Calderbank, Hanlon and Robinson consider the cases of block sizes that are congruent to 0 mod d and 1 mod d for fixed d . We derive a general formula for the representation of the symmetric group on the homology of posets of pa...

We will show that shellability, Cohen-Macaulayness and vertexde composability of a graded, planar poset P are all equivalent with the fact that P has the maximal possible number of edges. Also, for a such poset we will find an R−labelling with {1, 2} as the set of labels. Using this, we will obtain all essential linear inequalities for the flag h−vectors of shellable planar posets from [1]. AMS...

For every hypergraph on n vertices there is an associated subspace arrangement in R n called a hypergraph arrangement. We prove shellability for the intersection lattices of a large class of hypergraph arrangements. This class incorporates all the hypergraph arrangements which were previously shown to have shellable intersection lattices.