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April 2011 Some combinatorial properties of flag simplicial pseudomanifolds and spheres
Christos A. Athanasiadis
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Ark. Mat. 49(1): 17-29 (April 2011). DOI: 10.1007/s11512-009-0106-4


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 (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.

Funding Statement

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


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


Download Citation

Christos A. Athanasiadis. "Some combinatorial properties of flag simplicial pseudomanifolds and spheres." Ark. Mat. 49 (1) 17 - 29, April 2011.


Received: 6 April 2009; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1235.52020
MathSciNet: MR2784255
Digital Object Identifier: 10.1007/s11512-009-0106-4

Rights: 2009 © Institut Mittag-Leffler


Vol.49 • No. 1 • April 2011
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