Graduate Texts in Mathematics

Binomial Ideals

Authors: Herzog, Jürgen, Hibi, Takayuki, Ohsugi, Hidefumi

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  • 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
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eBook $59.99
price for USA in USD
  • ISBN 978-3-319-95349-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $79.99
price for USA in USD
Softcover $79.99
price for USA in USD
About this Textbook

This 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.

About the authors

Jürgen 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. 

Reviews

“This is a valuable resource for students and researchers entering this area of combinatorial commutative algebra.” (Thomas Kahle, Mathematical Reviews, November, 2019)

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-319-95349-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $79.99
price for USA in USD
Softcover $79.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Binomial Ideals
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
279
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-95349-6
DOI
10.1007/978-3-319-95349-6
Hardcover ISBN
978-3-319-95347-2
Softcover ISBN
978-3-030-07019-9
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIX, 321
Number of Illustrations
51 b/w illustrations, 4 illustrations in colour
Topics