Browsing Cornell Theses and Dissertations by Author "Chong, Kai Fong Ernest"

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Face Vectors And Hilbert Functions

Chong, Kai Fong Ernest (2015-08-17)

This dissertation builds upon two well-known theorems: Macaulay's theorem on the Hilbert functions of graded ideals, and the Kruskal-Katona theorem on the face vectors of simplicial complexes. There are four parts in the ...