单纯阶和弦
Simplicial orders and chordality
摘要：
在[14]和[3]的意义上的弦杂波是通过单纯阶定义的。他们的电路理想具有线性分辨率，与基场的特性无关。我们表明，任何贝蒂序列的理想与线性分辨率出现的贝蒂序列的电路理想，这样的弦杂波。与任何单纯阶相关联的是一个整数序列，我们称之为弦杂波的$λ$序列。表征了所有可能的$λ$ -序列。它们密切相关的希尔伯特函数的一个适当的标准分级$K$代数连接到弦杂波。利用弦杂波的$λ$序列，我们确定了电路理想的其它数值不变量，如$\textbf{h}$矢量和贝蒂数.
英文摘要：
Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear resolution appears as the Betti sequence of the circuit ideal of such a chordal clutter. Associated with any simplicial order is a sequence of integers which we call the $λ$-sequence of the chordal clutter. All possible $λ$-sequences are characterized. They are intimately related to the Hilbert function of a suitable standard graded $K$-algebra attached to the chordal clutter. By the $λ$-sequence of a chordal clutter we determine other numerical invariants of the circuit ideal, such as the $\textbf{h}$-vector and the Betti numbers.
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