科研之友
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摘要
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.
- 出版日期2011-10
