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Cover: 9783319953472 | Binomial Ideals | Jürgen Herzog (u. a.) | Buch | xix | Englisch | 2018
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Binomial Ideals
Buch von Jürgen Herzog (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xix
321 S.
51 s/w Illustr.
4 farbige Illustr.
321 p. 55 illus.
4 illus. in color.
ISBN-13: 9783319953472
ISBN-10: 3319953478
Sprache: Englisch
Herstellernummer: 978-3-319-95347-2
Einband: Gebunden
Autor: Herzog, Jürgen
Ohsugi, Hidefumi
Hibi, Takayuki
Auflage: 1st edition 2018
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 25 mm
Von/Mit: Jürgen Herzog (u. a.)
Erscheinungsdatum: 10.10.2018
Gewicht: 0,682 kg
Artikel-ID: 113909954
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xix
321 S.
51 s/w Illustr.
4 farbige Illustr.
321 p. 55 illus.
4 illus. in color.
ISBN-13: 9783319953472
ISBN-10: 3319953478
Sprache: Englisch
Herstellernummer: 978-3-319-95347-2
Einband: Gebunden
Autor: Herzog, Jürgen
Ohsugi, Hidefumi
Hibi, Takayuki
Auflage: 1st edition 2018
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 25 mm
Von/Mit: Jürgen Herzog (u. a.)
Erscheinungsdatum: 10.10.2018
Gewicht: 0,682 kg
Artikel-ID: 113909954
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