Hereditary properties and obstructions of simplicial complexes
نویسنده
چکیده
In this paper, we discuss the relation between shellability, sequentially CohenMacaulayness, and partitionability. Especially, our main concern is to see the difference of these properties when we require heredity. For a property 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 P, and we want to see the difference between hereditary-shellability, hereditary-sequential CohenMacaulayness, and hereditary-partitionability. 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 discussion on relations between these properties and h-triangles, especially, relations between partitionability and nonnegativity of h-triangles.
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