Some combinatorial properties of flag simplicial pseudomanifolds and spheres

Details Some combinatorial properties of flag simplicial pseudomanifolds and spheres Some combinatorial properties of flag simplicial pseudomanifolds and spheres

2008-07-28

arxiv.org/abs/0807.4369v3

Mathematics

Combinatorics

Final version, 11 pages. This version, which is somewhat shorter, contains a new result (Theorem 1.2)

Scientific paper

A simplicial complex $\Delta$ is called flag if all minimal nonfaces of $\Delta$ have at most two elements. The following are proved: First, if $\Delta$ is a flag simplicial pseudomanifold of dimension $d-1$, then the graph of $\Delta$ (i) is $(2d-2)$-vertex-connected and (ii) has a subgraph which is a subdivision of the graph of the $d$-dimensional cross-polytope. Second, the $h$-vector of a flag simplicial homology sphere $\Delta$ of dimension $d-1$ is minimized when $\Delta$ is the boundary complex of the $d$-dimensional cross-polytope.

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