Hereditary properties and obstructions of simplicial complexes (Designs, Codes, Graphs and Related Areas)
正泰 八森 · Kyoto University Research Information Repository (Kyoto University) · 2016
In this paper, we discuss the relation between shellability, sequentially Cohen- Macaulayness, and partitionability.Especially, our main concern is to see the difference of these properties when we require heredity.For a property $\mathcal{P}$ , we say a simplicial complex satisfies hereditary-P if the simplicial complex itself and all the restrictions to subsets of its vertex set satisfy the property $\mathcal{P}$ , and we want to see the difference between hereditary-shellability, hereditary-sequential Cohen- Macaulayness, and $hereditary-1$)artitionability In this paper we briefly review on the relations and gaps between shellability, sequential Cohen-Macaulayness and partitionability, as well as their hereditary versions.Additionally, we provide a dis- cussion on relations between these properties and $h$ -triangles, especially, relations between partitionability and nonnegativity of $h$ -triangles.