Binomial Ideals

• Main Authors: Herzog, Jürgen (Author, http://id.loc.gov/vocabulary/relators/aut), Hibi, Takayuki (http://id.loc.gov/vocabulary/relators/aut), Ohsugi, Hidefumi (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Graduate Texts in Mathematics, 279
• Subjects: Commutative algebra.; Commutative rings.; Convex geometry .; Discrete geometry.; Combinatorics.; Commutative Rings and Algebras.; Convex and Discrete Geometry.

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 o...

Table of Contents:

• Part 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.