147 research outputs found
Resolutions of letterplace ideals of posets
We investigate resolutions of letterplace ideals of posets. We develop
topological results to compute their multigraded Betti numbers, and to give
structural results on these Betti numbers. If the poset is a union of no more
than chains, we show that the Betti numbers may be computed from simplicial
complexes of no more than vertices. We also give a recursive procedure to
compute the Betti diagrams when the Hasse diagram of has tree structure.Comment: 21 page
Saturated simplicial complexes
AbstractAmong 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
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