dc.contributor.author | Hoefel, Andrew Harald | |
dc.date.accessioned | 2011-08-12T11:19:57Z | |
dc.date.available | 2011-08-12T11:19:57Z | |
dc.date.issued | 2011-08-12 | |
dc.identifier.uri | http://hdl.handle.net/10222/13998 | |
dc.description.abstract | In this thesis, we study Hilbert functions of monomial ideals in the polynomial ring and the Kruskal-Katona ring. In particular, we classify Gotzmann edge ideals and, more generally, Gotzmann squarefree monomial ideals. In addition, we discuss Betti numbers of Gotzmann ideals and measure how far certain edge ideals are from Gotzmann. This thesis also contains a thorough account the combinatorial relationship between lex segments and Macaulay representations of their dimensions and codimensions. | en_US |
dc.language.iso | en | en_US |
dc.subject | combinatorial commutative algebra | en_US |
dc.subject | Hilbert functions | en_US |
dc.subject | monomial ideals | en_US |
dc.title | Hilbert Functions in Monomial Algebras | en_US |
dc.date.defence | 2011-07-25 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.external-examiner | Irena Swanson | en_US |
dc.contributor.graduate-coordinator | Sara Faridi | en_US |
dc.contributor.thesis-reader | Keith Johnson | en_US |
dc.contributor.thesis-reader | Richard Nowakowski | en_US |
dc.contributor.thesis-supervisor | Sara Faridi | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Yes | en_US |
dc.contributor.copyright-release | Yes | en_US |