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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

Abstract

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.

Dedication

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

Citation

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

Information

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

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Vol.49 • No. 1 • April 2011
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