Hilbert Functions in Monomial Algebras

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