To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to an interesting quotient ring. Our main ...

Let I ⊂ K[x1, . . . , xn] be a zero-dimensional monomial ideal, and ∆(I) be the simplicial complex whose Stanley–Reisner ideal is the polarization of I. It follows from a result of Soleyman Jahan that ∆(I) is shellable. We give a new short proof of this fact by providing an explicit shelling. Moreover, we show that ∆(I) is even vertex decomposable. The ideal L(I), which is defined to be the Sta...

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...