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Binomial ideals

Herzog, Jurgen.

Binomial ideals

Record Type:	Electronic resources : Monograph/item
Title/Author:	Binomial idealsby Jurgen Herzog, Takayuki Hibi, Hidefumi Ohsugi.
Author:	Herzog, Jurgen.
other author:	Hibi, Takayuki.
Published:	Cham :Springer International Publishing :2018.
Description:	xix, 321 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Commutative algebra.
Online resource:	https://doi.org/10.1007/978-3-319-95349-6
ISBN:	9783319953496$q(electronic bk.)

Binomial ideals
Herzog, Jurgen.

Binomial ideals[electronic resource] /by Jurgen Herzog, Takayuki Hibi, Hidefumi Ohsugi. - Cham :Springer International Publishing :2018. - xix, 321 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2790072-5285 ;. - Graduate texts in mathematics ;129..

Part I: Basic Concepts -- Polynomial Rings and Grobner 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.

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 Grobner 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.

ISBN: 9783319953496$q(electronic bk.)

Standard No.: 10.1007/978-3-319-95349-6doiSubjects--Topical Terms:

190842
Commutative algebra.

LC Class. No.: QA251.3 / .H479 2018

Dewey Class. No.: 512.44

Binomial ideals
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245 1 0 $a Binomial ideals $h [electronic resource] / $c by Jurgen Herzog, Takayuki Hibi, Hidefumi Ohsugi.
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300 $a xix, 321 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 279
505 0 $a Part I: Basic Concepts -- Polynomial Rings and Grobner 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.
520 $a 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 Grobner 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.
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650 0 $a Binomial theorem. $3 823448
650 1 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a Combinatorics. $3 274788
700 1 $a Hibi, Takayuki. $3 509077
700 1 $a Ohsugi, Hidefumi. $3 823447
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950 $a Mathematics and Statistics (Springer-11649)