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2019744217
9783030070199 (Pbk)
10.1007/978-3-319-95349-6
doi
(DE-He213)978-3-319-95349-6
DLC
eng
pn
rda
IISERB
MAT002010
bisacsh
PBF
bicssc
PBF
thema
512.44 H44B
23
Herzog, Jurgen.
28098
Binomial Ideals
by Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi.
Switzerland:
Springer Nature,
2018.
XIX, 321 p.
55 illustrations, 4 illustrations in color.
Graduate Texts in Mathematics,
0072-5285 ;
279
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.
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.
Combinatorics.
28099
Commutative algebra.
28100
Commutative rings.
28101
Convex geometry.
28102
Discrete geometry.
28103
Commutative Rings and Algebras.
28104
Combinatorics.
28099
Convex and Discrete Geometry.
28105
Hibi, Takayuki.
28106
Ohsugi, Hidefumi.
28107
Print version:
Binomial ideals
9783319953472
(DLC) 2018949912
Printed edition:
9783030070199
Printed edition:
9783319953472
Printed edition:
9783319953489
Graduate Texts in Mathematics,
279
28108
0
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origres
u
ncip
20
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BK
0
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