Arkiv för Matematik

  • Ark. Mat.
  • Volume 49, Number 2 (2011), 335-350.

Balanced complexes and complexes without large missing faces

Michael Goff, Steven Klee, and Isabella Novik

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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.


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

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Ark. Mat., Volume 49, Number 2 (2011), 335-350.

Received: 10 July 2009
First available in Project Euclid: 31 January 2017

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2010 © Institut Mittag-Leffler


Goff, Michael; Klee, Steven; Novik, Isabella. Balanced complexes and complexes without large missing faces. Ark. Mat. 49 (2011), no. 2, 335--350. doi:10.1007/s11512-009-0119-z.

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