Some combinatorial properties of flag simplicial pseudomanifolds and spheres

Christos A. Athanasiadis Department of Mathematics, University of Athens

Combinatorics Convex and Discrete Geometry mathscidoc:1701.06002

Arkiv for Matematik, 49, (1), 17-29, 2009.4
A simplicial complex Δ is called$flag$if all minimal nonfaces of Δ have at most two elements. The following are proved: First, if Δ is a flag simplicial pseudomanifold of dimension$d$−1, then the graph of Δ (i) is (2$d$−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 Δ of dimension$d$−1 is minimized when Δ is the boundary complex of the$d$-dimensional cross-polytope.
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@inproceedings{christos2009some,
  title={Some combinatorial properties of flag simplicial pseudomanifolds and spheres},
  author={Christos A. Athanasiadis},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203628735420989},
  booktitle={Arkiv for Matematik},
  volume={49},
  number={1},
  pages={17-29},
  year={2009},
}
Christos A. Athanasiadis. Some combinatorial properties of flag simplicial pseudomanifolds and spheres. 2009. Vol. 49. In Arkiv for Matematik. pp.17-29. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203628735420989.
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