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dc.contributor.authorErey, Nursel
dc.date.accessioned2015-08-13T11:40:45Z
dc.date.available2015-08-13T11:40:45Z
dc.identifier.urihttp://hdl.handle.net/10222/59856
dc.description.abstractIn 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.en_US
dc.language.isoenen_US
dc.subjectMonomial idealsen_US
dc.subjectMinimal free resolutionsen_US
dc.subjectBetti numbersen_US
dc.subjectSimplicial complexesen_US
dc.titleOn the combinatorics of resolutions of monomial idealsen_US
dc.typeThesisen_US
dc.date.defence2015-08-04
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeDoctor of Philosophyen_US
dc.contributor.external-examinerSean Sather-Wagstaffen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerKeith Johnsonen_US
dc.contributor.thesis-readerRobert Pareen_US
dc.contributor.thesis-supervisorSara Faridien_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsYesen_US
dc.contributor.copyright-releaseNoen_US
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