We construct the first linear strand of the minimal free resolutions of edge ideals of d-partite d-uniform clutters. We show that the first linear strand of such ideals are supported on relative simplicial complexes. In the case that the edge ideals of such clutters have linear resolutions, we give an explicit and surprisingly simple description of their minimal free resolutions, generalizing known resolutions for edge ideals of Ferrers graphs and hypergraphs and co-letterplace ideals. As an application, we show that the Lyubeznik numbers that appear on the last column of the Lyubeznik table of the cover ideal of such clutters are Betti numbers of certain simplicial complexes. Furthermore, we restate a characterization for edge ideals of d-partite d-uniform clutters which have linear resolutions based on the recent characterization of arithmetically Cohen-Macaulay sets of points in multiprojective spaces.

我们构造了d部分d均匀杂波的边缘理想的最小自由分辨率的第一条线性链。我们证明了这样的理想的第一线性链在相对简单复数上得到支持。在此类杂波的边缘理想具有线性分辨率的情况下，我们对它们的最小自由分辨率进行了明确而出乎意料的简单描述，归纳了费雷尔图和超图的边缘理想以及共同字母理想的已知分辨率。作为一个应用程序，我们证明出现在此类杂波的理想封面的Lyubeznik表的最后一列上的Lyubeznik数是某些简单复数的Betti数。此外，我们重申d -partite边理想的特征d-一致的杂波，具有线性分辨率，基于最近在多投影空间中的Cohen-Macaulay点集的算术表征。