Combinatorial Commutative Algebra
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Combinatorial Commutative Algebra
Author: Ezra Miller
language: en
Publisher: Springer Science & Business Media
Release Date: 2005-06-21
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Combinatorics and Commutative Algebra
Author: Richard P. Stanley
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-13
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.
Combinatorial Commutative Algebra
Author: Ezra Miller
language: en
Publisher: Springer Science & Business Media
Release Date: 2005-11-13
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.