Abstract
Among shellable complexes a certain class has maximal modular homology, and these are the so-called saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the p-rank of incidence matrices and via the structure of links. We show that rank-selected subcomplexes of saturated complexes are also saturated, and that order complexes of geometric lattices are saturated.
Original language | English |
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Pages (from-to) | 149-179 |
Number of pages | 31 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 109 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2005 |