2015•DalSpace (Dalhousie University)Requires access
On the combinatorics of resolutions of monomial ideals
Nursel Erey
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Abstract
In this thesis, we investigate the relation between invariants of minimal free resolutions of monomial ideals and combinatorial properties of simplicial complexes. We provide a sufficient combinatorial condition for monomial ideals to have nonzero Betti numbers and show that such a condition completely characterizes Betti numbers of facet ideals of simplicial forests. We also present a new approach to computing Betti numbers of path ideals of certain graph classes.