Saturated simplicial complexes

V. B. Mnukhin, J. Siemons

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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 languageEnglish
Pages (from-to)149-179
Number of pages31
JournalJournal of Combinatorial Theory, Series A
Issue number1
Publication statusPublished - 2005

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