Balanced complexes and complexes without large missing faces
Balanced complexes and complexes without large missing faces
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平衡的复合体和复合体，没有大的缺失面
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
I. Novik
中科院分区：
文献类型：
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作者：
Michael Goff;S. Klee;I. Novik
研究了维数大于i的无缺面单纯复形的面数。证明了在所有这样的具有非零顶同调的（d−1）维复形中，某个多面体球面具有分量最小f-向量;而且，在所有这样的2-Cohen-Macaulay（2-CM）复形中，同一个球面具有分量最小h-向量。证明了旗（d−1）维2-CM复形的l-骨架是2（d− 1）-CM，而旗分段线性（d−1）-球面的l-骨架是2（d− 1）-同伦CM.此外，2-CM平衡复形的面数的紧下界的维数和顶点的数量建立。
The face numbers of simplicial complexes without missing faces of dimension larger than i are studied. It is shown that among all such (d−1)-dimensional complexes with non-vanishing top homology, a certain polytopal sphere has the componentwise minimal f-vector; and moreover, among all such 2-Cohen–Macaulay (2-CM) complexes, the same sphere has the componentwise minimal h-vector. It is also verified that the l-skeleton of a flag (d−1)-dimensional 2-CM complex is 2(d−l)-CM, while the l-skeleton of a flag piecewise linear (d−1)-sphere is 2(d−l)-homotopy CM. In addition, tight lower bounds on the face numbers of 2-CM balanced complexes in terms of their dimension and the number of vertices are established.