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OverviewThis textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource. Full Product DetailsAuthor: Jürgen Herzog , Takayuki Hibi , Hidefumi OhsugiPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2018 Volume: 279 Weight: 0.682kg ISBN: 9783319953472ISBN 10: 3319953478 Pages: 321 Publication Date: 10 October 2018 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPart I: Basic Concepts.- Polynomial Rings and Gröbner Bases.- Review of Commutative Algebra.- Part II:Binomial Ideals and Convex Polytopes.- Introduction to Binomial Ideals.- Convex Polytopes and Unimodular Triangulations.- Part III. Applications in Combinatorics and Statistics- Edge Polytopes and Edge Rings.- Join-Meet Ideals of Finite Lattices.- Binomial Edge Ideals and Related Ideals.- Ideals Generated by 2-Minors.- Statistics.- References.- Index.Reviews“This is a valuable resource for students and researchers entering this area of combinatorial commutative algebra.” (Thomas Kahle, Mathematical Reviews, November, 2019) This is a valuable resource for students and researchers entering this area of combinatorial commutative algebra. (Thomas Kahle, Mathematical Reviews, November, 2019) Author InformationJürgen Herzon is a professor at the University of Duisburg-Essen and coauthor of Monomial Ideals (2011) with Takayuki Hibi. Takayuki Hibi is a professor at Osaka University. Hidefumi Ohsugi is a professor at Rikkyo University. Tab Content 6Author Website:Countries AvailableAll regions |
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