Simplicial complexes with many facets are vertex decomposable
arxiv(2024)
摘要
Let Δ be a pure simplicial complex on n vertices having dimension
d and codimension c = n-d-1 in the simplex. Terai and Yoshida proved that
if the number of facets of Δ is at least nc-2c+1, then
Δ is Cohen-Macaulay. We improve this result by showing that these
hypotheses imply the stronger condition that Δ is vertex decomposable.
We give examples to show that this bound is optimal, and that the conclusion
cannot be strengthened to the class of matroids or shifted complexes. We
explore an application to Simon's Conjecture and discuss connections to other
results from the literature.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要