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Monomial Ideals

✍ Scribed by J. Herzog; Takayuki Hibi

Publisher
Springer
Year
2010
Tongue
English
Leaves
311
Series
Graduate Texts in Mathematics
Category
Library
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✦ Synopsis

Part I GrοΏ½bner bases: Monomial Ideals.- A short introduction to GrοΏ½bner 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

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