Arkiv för Matematik

Some combinatorial properties of flag simplicial pseudomanifolds and spheres

Christos A. Athanasiadis

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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 (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 Δ of dimension d−1 is minimized when Δ is the boundary complex of the d-dimensional cross-polytope.


Dedicated to Anders Björner on the occasion of his sixtieth birthday.


Supported by the 70/4/8755 ELKE Research Fund of the University of Athens.

Article information

Ark. Mat., Volume 49, Number 1 (2011), 17-29.

Received: 6 April 2009
First available in Project Euclid: 31 January 2017

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2009 © Institut Mittag-Leffler


Athanasiadis, Christos A. Some combinatorial properties of flag simplicial pseudomanifolds and spheres. Ark. Mat. 49 (2011), no. 1, 17--29. doi:10.1007/s11512-009-0106-4.

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