论文标题
准林 - 朴素复合物和几乎Cohen-Macaulay
Quasi-forest simplicial complexes and almost Cohen-Macaulay
论文作者
论文摘要
在本文中，我们研究了准森林简单综合体，并定义了简单$ k $ -cycle的概念（用$ \ Mathcal {s} _K $表示）和simplicial $ k $ - 点（由$ \ Mathcal {p} {p}表示，我们表明，当它没有任何$ \ MATHCAL {p} _k $和任何$ \ Mathcal {s} _k $ for $ k \ geq 3 $时，且仅当它没有任何$ \ mathcal {p} _k $和任何$ \ mathcal {p} _k $时，就表明了一个简单的复杂$δ$。此外，我们还表征了几乎Cohen-Macaulay准林 - 森林简单复合物。最后，我们证明循环图$ g = C_n $几乎是Cohen-Macaulay，并且仅当$ n = 3,4,5,6,7,8,9,11 $。
In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial $k$-cycle (denoted by $\mathcal{S}_k$) and simplicial $k$-point (denoted by $\mathcal{P}_k$). We show that a simplicial complex $Δ$ is quasi-forest if and only if it does not have any $\mathcal{P}_k$ and any $\mathcal{S}_k$ for $k\geq 3$. Furthermore we characterize almost Cohen-Macaulay quasi-forest simplicial complexes. In the end we show that the cycle graph $G=C_n$ is almost Cohen-Macaulay if and only if $n=3,4,5,6,7,8,9,11$.
