论文标题
相对简单络合物及其H-向量上可撒的瓷砖
Shellable tilings on relative simplicial complexes and their h-vectors
论文作者
论文摘要
在有限的简单络合物上进行的H式薄层是其几何形状实现的分区，最大简单被剥夺了几个编成的一面脸，并可能剩下的最高的编成词。在最后一个情况下，瓷砖被认为至关重要。因此，通过封闭或半开放的间隔，H薄层诱导其面部poset的分区。我们证明了在最大简单上有限的许多恒星细分之后，在每个有限的简单复合物上都存在H倾斜度。这些瓷砖还可以壳。我们还证明，由其H-vector编码的瓷砖使用的每种类型的瓷砖数量取决于其使用的每个索引的临界图块的数量，由其临界向量编码。在封闭的三角歧管的情况下，这些向量满足了一些倾向性特性。我们最终研究了在任何恒星细分下的瓷砖行为。
An h-tiling on a finite simplicial complex is a partition of its geometric realization by maximal simplices deprived of several codimension one faces together with possibly their remaining face of highest codimension. In this last case, the tiles are said to be critical. An h-tiling thus induces a partitioning of its face poset by closed or semi-open intervals. We prove the existence of h-tilings on every finite simplicial complex after finitely many stellar subdivisions at maximal simplices. These tilings are moreover shellable. We also prove that the number of tiles of each type used by a tiling, encoded by its h-vector, is determined by the number of critical tiles of each index it uses, encoded by its critical vector. In the case of closed triangulated manifolds, these vectors satisfy some palindromic property. We finally study the behavior of tilings under any stellar subdivision.
