Chordal and Sequentially Cohen-Macaulay Clutters
Chordal and Sequentially Cohen-Macaulay Clutters
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DOI：
10.37236/695
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发表时间：
2009-11
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影响因子：
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通讯作者：
Russ Woodroofe
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文献类型：
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作者：
Russ Woodroofe
我们将弦的定义从图扩展到杂波。得到的族推广了弦图和拟阵，并且遵循许多相同的代数和几何性质。具体地说，弦杂波的独立复合体是可剥离的，因此是顺序的Cohen-Macaulay；并且对这种杂波的某种补充的电路理想具有线性分辨率。最小非弦杂波也与可剥性障碍密切相关，我们给出了这类障碍的一些通用族，并通过计算给出了6个顶点上所有可剥离性障碍的分类。
We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal non-chordal clutters are also closely related to obstructions to shellability, and we give some general families of such obstructions, together with a classification by computation of all obstructions to shellability on 6 vertices.