Arkiv för Matematik
- Ark. Mat.
- Volume 49, Number 2 (2011), 335-350.
Balanced complexes and complexes without large missing faces
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(d−l)-CM, while the l-skeleton of a flag piecewise linear (d−1)-sphere is 2(d−l)-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.
Ark. Mat., Volume 49, Number 2 (2011), 335-350.
Received: 10 July 2009
First available in Project Euclid: 31 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.afm/1485907140