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October 2011 Balanced complexes and complexes without large missing faces
Michael Goff, Steven Klee, Isabella Novik
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Ark. Mat. 49(2): 335-350 (October 2011). DOI: 10.1007/s11512-009-0119-z


The face numbers of simplicial complexes without missing faces of dimension larger than i are studied. It is shown that among all such (d−1)-dimensional complexes with non-vanishing top homology, a certain polytopal sphere has the componentwise minimal f-vector; and moreover, among all such 2-Cohen–Macaulay (2-CM) complexes, the same sphere has the componentwise minimal h-vector. It is also verified that the l-skeleton of a flag (d−1)-dimensional 2-CM complex is 2(dl)-CM, while the l-skeleton of a flag piecewise linear (d−1)-sphere is 2(dl)-homotopy CM. In addition, tight lower bounds on the face numbers of 2-CM balanced complexes in terms of their dimension and the number of vertices are established.

Funding Statement

Novik’s research was partially supported by an Alfred P. Sloan Research Fellowship and NSF grant DMS-0801152.


Download Citation

Michael Goff. Steven Klee. Isabella Novik. "Balanced complexes and complexes without large missing faces." Ark. Mat. 49 (2) 335 - 350, October 2011.


Received: 10 July 2009; Published: October 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1256.05259
MathSciNet: MR2826947
Digital Object Identifier: 10.1007/s11512-009-0119-z

Rights: 2010 © Institut Mittag-Leffler


Vol.49 • No. 2 • October 2011
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