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Monomial Ideals

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Part I Gr�bner bases: Monomial Ideals.- A short introduction to Gr�bner bases.- Monomial orders and weights.- Generic initial ideals.- The exterior algebra.- Part II: Hilbert functions and resolutions.- Hilbert functions and the theorems of Macaulay and Kruskal-Katona.- Resolutions of monomial ideals and the Eliahou-Kervaire formula.- Alexander duality and resolutions.- Part III Combinatorics: Alexander duality and finite graphs.- Powers of monomial ideals.- Shifting theory.- Discrete Polymatroids.- Some homological algebra.- Geometry

Author(s): J. Herzog; Takayuki Hibi
Series: Graduate Texts in Mathematics
Publisher: Springer
Year: 2010

Language: English
Pages: 305