Overview
- Presents a thorough study of binomial ideals and their applications, working from the basics through to current research
- Offers an accessible introduction to the area for combinatorialists and statisticians, building only on the basics of commutative algebra.
- Explores the new research area of algebraic statistics and its relation to toric ideals and their Gröbner bases
Part of the book series: Graduate Texts in Mathematics (GTM, volume 279)
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Table of contents (9 chapters)
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Front Matter
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Basic Concepts
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Front Matter
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Binomial Ideals and Convex Polytopes
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Front Matter
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Applications in Combinatorics and Statistics
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
Authors and Affiliations
About the authors
Takayuki Hibi is a professor at Osaka University.
Hidefumi Ohsugi is a professor at Rikkyo University.
Bibliographic Information
Book Title: Binomial Ideals
Authors: Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-95349-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-95347-2Published: 10 October 2018
Softcover ISBN: 978-3-030-07019-9Published: 31 January 2019
eBook ISBN: 978-3-319-95349-6Published: 28 September 2018
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XIX, 321
Number of Illustrations: 51 b/w illustrations, 4 illustrations in colour
Topics: Commutative Rings and Algebras, Convex and Discrete Geometry, Combinatorics