Titlebook: Binomial Ideals; Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi Textbook 2018 Springer International Publishing AG, part of Springer Nature 2

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Edge Polytopes and Edge Ringsan edge polytope is normal if and only if it possesses a unimodular covering (Theorem 5.20). Finally, in Section 5.5, Gröbner bases of toric ideals arising from bipartite graphs will be discussed. In particular, we show that the toric ideal of the edge ring of a bipartite graph is generated by quadr

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Ccu106

Statistics9.4, we study the toric rings and ideals of hierarchical models. In particular, the toric rings of no .-way interaction models are related to the notion of .th Lawrence liftings. Finally, in Section 9.5, as generalizations of Segre products and Veronese subrings, the so-called Segre–Veronese configu

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0072-5285 sults 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 statisti978-3-030-07019-9978-3-319-95349-6Series ISSN 0072-5285 Series E-ISSN 2197-5612

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Textbook 2018stics.  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 statisti

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Review of Commutative Algebraeview on graded rings, Hilbert functions, and Hilbert series, and introduce the multiplicity and the .-invariant of a graded module. The Krull dimension of a graded module will be defined in terms of its Hilbert series. We will give various characterizations of the depth of a module and its relation

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Left-Atrium

Convex Polytopes and Unimodular Triangulationsatment of triangulations of convex polytopes is systematically developed. In Section 4.1 we recall fundamental materials on convex polytopes and summarize basic facts without their proofs. The highlight of Chapter 4 is Section 4.2, where unimodular triangulations of convex polytopes are introduced a