Download E-books Monomial Ideals: 260 (Graduate Texts in Mathematics) PDF

By Jürgen Herzog

This publication demonstrates present tendencies in examine on combinatorial and computational commutative algebra with a first-rate emphasis on themes on the topic of monomial ideals.

Providing an invaluable and quickly advent to parts of analysis spanning those fields, Monomial beliefs is divided into 3 components. half I bargains a brief creation to the fashionable idea of Gröbner bases in addition to the distinct learn of primary preliminary beliefs. half II offers Hilbert capabilities and resolutions and a few of the combinatorics concerning monomial beliefs together with the Kruskal—Katona theorem and algebraic features of Alexander duality. half III discusses combinatorial functions of monomial beliefs, supplying a beneficial evaluate of a few of the important tendencies in algebraic combinatorics. major topics comprise facet beliefs of finite graphs, powers of beliefs, algebraic transferring thought and an advent to discrete polymatroids. idea is complemented by means of a couple of examples and routines all through, bringing the reader to a deeper knowing of strategies explored in the text.

Self-contained and concise, this publication will attract a variety of readers, together with PhD scholars on complex classes, skilled researchers, and combinatorialists and non-specialists with a uncomplicated wisdom of commutative algebra.

Since their first assembly in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka collage, Japan), have labored jointly on a few learn initiatives, of which fresh effects are awarded during this monograph.

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