论文标题
$ f $ - 理想的Cohen-Macaulay物业
The Cohen-Macaulay Property of $f$-ideals
论文作者
论文摘要
对于正整数$ d <n $，让$ [n] _d = \ {a \ in 2^{[n]} \ mid | a | = d \} $其中$ [n] =：\ {1,2，\ ldots，n \} $。对于纯$ f $ -simplicial复合物$δ$，以便$ {\ rm dim}（δ）= {\ rm dim}（Δ^c）$和$ \ nathcal {f}（δ）\ cap \ cap \ cap \ nathcal {f}（f}（δ^c）（δ^c）只有当它具有线性分辨率时。对于$ d $二维纯$ f $ -simplicial complex $δ$，以至于$δ=：\ langle f \ f \ mid f \ in [n] _d \ smallSetMinus \ smallclcal \ mathcal f（Δ）\ rangle $ rangle $是$ f $ f $ -simplicial complect and $ simplicial complect，我们是$ i的$ i（IS $ i i i是$ i（IS）。 $ i（δ'）$具有线性分辨率。
For positive integers $d<n$, let $[n]_d=\{A\in 2^{[n]}\mid |A|=d\}$ where $[n]=:\{1,2,\ldots, n\}$. For a pure $f$-simplicial complex $Δ$ such that ${\rm dim}(Δ)={\rm dim}(Δ^c)$ and $\mathcal{F}(Δ)\cap \mathcal{F}(Δ^c)=\emptyset$, we prove that the facet ideal $I(Δ)$ is Cohen-Macaulay if and only if it has linear resolution. For a $d$-dimensional pure $f$-simplicial complex $Δ$ such that $Δ'=:\langle F\mid F\in [n]_d\smallsetminus \mathcal F(Δ)\rangle$ is an $f$-simplicial complex, we prove that $I(Δ^c)$ is Cohen-Macaulay if and only if $I(Δ')$ has linear resolution.
