147 research outputs found

    Resolutions of letterplace ideals of posets

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    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 cc chains, we show that the Betti numbers may be computed from simplicial complexes of no more than cc vertices. We also give a recursive procedure to compute the Betti diagrams when the Hasse diagram of PP has tree structure.Comment: 21 page

    Saturated simplicial complexes

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    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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