03336cam a22004695i 450000100090000000300040000900500170001300600190003000700150004900800410006401000170010502000240012202400350014603500320018104000300021307200230024307200160026607200150028208200200029710000200031724500740033726000420041130000620045349000530051550504740056852013640104265000190240665000250242565000230245065000210247365000230249465000360251765000190255365000340257270000200260670000220262677600700264877600360271877600360275477600360279083000400282621676298OSt20220215105057.0m |o d | cr |||||||||||180928s2018 gw |||| o |||| 0|eng a 2019744217 a9783030070199 (Pbk)7 a10.1007/978-3-319-95349-62doi a(DE-He213)978-3-319-95349-6 aDLCbengepnerdacIISERB 7aMAT0020102bisacsh 7aPBF2bicssc 7aPBF2thema04a512.44 H44B2231 aHerzog, Jurgen.10aBinomial Ideals cby Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi. aSwitzerland:bSpringer Nature,c2018. aXIX, 321 p. c55 illustrations, 4 illustrations in color.1 aGraduate Texts in Mathematics,x0072-5285 ;v2790 aPart 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. aThis 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. 0aCombinatorics. 0aCommutative algebra. 0aCommutative rings. 0aConvex geometry. 0aDiscrete geometry.14aCommutative Rings and Algebras.24aCombinatorics.24aConvex and Discrete Geometry.1 aHibi, Takayuki.1 aOhsugi, Hidefumi.08iPrint version:tBinomial idealsz9783319953472w(DLC) 201894991208iPrinted edition:z978303007019908iPrinted edition:z978331995347208iPrinted edition:z9783319953489 0aGraduate Texts in Mathematics,v279