Combinatorial Commutative Algebra
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Combinatorial Commutative Algebra
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Author : Ezra Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-13
Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-13 with Mathematics categories.
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.
Combinatorial Commutative Algebra
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Author : Ezra Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21
Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Combinatorial Aspects Of Commutative Algebra
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Author : Viviana Ene
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-25
Combinatorial Aspects Of Commutative Algebra written by Viviana Ene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-25 with Mathematics categories.
This volume contains the proceedings of the Exploratory Workshop on Combinatorial Commutative Algebra and Computer Algebra, which took place in Mangalia, Romania on May 29-31, 2008. It includes research papers and surveys reflecting some of the current trends in the development of combinatorial commutative algebra and related fields. This volume focuses on the presentation of the newest research results in minimal resolutions of polynomial ideals (combinatorial techniques and applications), Stanley-Reisner theory and Alexander duality, and applications of commutative algebra and of combinatorial and computational techniques in algebraic geometry and topology. Both the algebraic and combinatorial perspectives are well represented and some open problems in the above directions have been included.
Combinatorics And Commutative Algebra
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Author : Richard Stanley
language : en
Publisher: Birkhäuser
Release Date : 1996-03-01
Combinatorics And Commutative Algebra written by Richard Stanley and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-01 with Mathematics categories.
* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In this new edition, the author further develops some interesting properties of face rings with application to combinatorics
Combinatorics And Commutative Algebra
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Author : Richard P. Stanley
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Combinatorics And Commutative Algebra written by Richard P. Stanley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Mathematics categories.
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
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Author : Ezra Miller
language : en
Publisher: Springer
Release Date : 2008-11-01
Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Progress In Commutative Algebra 1
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Author : Christopher Francisco
language : en
Publisher: Walter de Gruyter
Release Date : 2012-04-26
Progress In Commutative Algebra 1 written by Christopher Francisco and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.
Computations And Combinatorics In Commutative Algebra
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Author : Anna M. Bigatti
language : en
Publisher: Springer
Release Date : 2017-03-14
Computations And Combinatorics In Commutative Algebra written by Anna M. Bigatti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-14 with Mathematics categories.
Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.
Combinatorial Commutative Algebra
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Author : Mathematisches Forschungsinstitut Oberwolfach
language : en
Publisher:
Release Date : 2004
Combinatorial Commutative Algebra written by Mathematisches Forschungsinstitut Oberwolfach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Computational Commutative Algebra And Combinatorics
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Author : Takayuki Hibi
language : en
Publisher:
Release Date : 2002
Computational Commutative Algebra And Combinatorics written by Takayuki Hibi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This volume constitutes the proceedings of the International Conference on ``Computational Commutative Algebra and Combinatorics'' held in Osaka, Japan. It contains excellent survey articles and research papers on various topics related to the theme of the conference. Of particular interest are two survey articles, ``Algebraic Shifting'' by Gil Kalai and ``Generic Initial Ideals and Graded Betti Numbers'' by Jurgen Herzog. The volume is suitable for graduate students and researchmathematicians interested in discrete mathematics. Information for our distributors: Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. All commercial channel discounts apply.