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Hilbert Functions in Monomial Algebras

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:NSHD.ca#10222/13998
Date25 July 2011
CreatorsHoefel, Andrew Harald
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish

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