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Combinatorial Aspects Of Commutative Algebra

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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry by Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen Book Summary:

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.

Combinatorial Aspects of Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Aspects of Commutative Algebra by Viviana Ene,Ezra Miller Book Summary:

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.

Geometric And Combinatorial Aspects Of Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Geometric And Combinatorial Aspects Of Commutative Algebra by Jurgen Herzog,Gaetana Restuccia Book Summary:

This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable idea

Geometric And Combinatorial Aspects Of Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Geometric And Combinatorial Aspects Of Commutative Algebra by Jurgen Herzog,Gaetana Restuccia Book Summary:

This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable ideals, and free resolutions.

Combinatorics and Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorics and Commutative Algebra by Richard P. Stanley Book Summary:

* 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

Algebraic and Combinatorial Aspects of Tropical Geometry

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Algebraic and Combinatorial Aspects of Tropical Geometry by Erwan Brugalle,Maria Angelica Cueto,Alicia Dickenstein,Eva-Maria Feichtner,Ilia Itenberg Book Summary:

This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mat

Combinatorics of Determinantal Ideas

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorics of Determinantal Ideas by N.A Book Summary:

Download or read Combinatorics of Determinantal Ideas book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Progress in Commutative Algebra 1

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Progress in Commutative Algebra 1 by Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev Book Summary:

This is the first of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University meeting. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This fist volume concentrates on combinatorics and homology.

Computations and Combinatorics in Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Computations and Combinatorics in Commutative Algebra by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Book Summary:

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.

Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Commutative Algebra by Alberto Corso,Philippe Gimenez,Maria Vaz Pinto,Santiago Zarzuela Book Summary:

Packed with contributions from international experts, Commutative Algebra: Geometric, Homological, Combinatorial, and Computational Aspects features new research results that borrow methods from neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation, and topology. This book consists of articles presented during two conferences held in Spain and Portugal in June, 2003. It encompasses a variety of topics, including blowup algebras, Castelnuovo-Mumford regularity, integral closure and normality, Koszul homology, liaison theory, multiplicities, polarization, and reductions of ideals. This comprehensive volume will stimulate further research in the field.

Combinatorial Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Book Summary:

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Combinatorial Aspects of Lie Superalgebras

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Aspects of Lie Superalgebras by Alexander A. Mikhalev,Andrej A. Zolotykh Book Summary:

Combinatorial Aspects of Lie Superalgebras emphasizes the algorithmic and computational aspects of the combinatorial techniques of Lie superalgebras. It is written primarily for mathematicians and scientists who do not have a background in the field of infinite dimensional Lie superalgebras, but who realize the potential uses of the results. Consequently, the discussions provided on the applications of Lie superalgebras theory are clear and comprehensive and, throughout the text, primary attention is given to algorithms and examples. The examples illustrate theoretical results, and the algorithms, which can be used for symbolic calculations with Lie superalgebras, are based on basic and generally applicable rules and theorems. Combinatorial Aspects of Lie Superalgebras contains comprehensive literature citations and provides an excellent reference on the techniques and results of combinatorial theory of Lie superalgebras. Programs that have been developed by the authors for computation are included on a diskette at the back of the book, and complete directions for use are provided.

Combinatorial and Computational Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial and Computational Algebra by Kai-Yuen Chan,Alexander A. Mikhalev,Man-Keung Siu,Jie-Tai Yu,Efim I. Zelmanov Book Summary:

This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra held at the University of Hong Kong (China). The conference was part of the Algebra Program at the Institute of Mathematical Research and the Mathematics Department at the University of Hong Kong. Topics include recent developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and non associative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory. This volume can serve as a solid introductory guide for advanced graduate students, as well as a rich and up-to-date reference source for contemporary researchers in the field.

Algebraic Combinatorics

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Algebraic Combinatorics by Richard P. Stanley Book Summary:

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.

Monomial Ideals

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Monomial Ideals by Jürgen Herzog,Takayuki Hibi Book Summary:

This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.

Combinatorial Commutative Algebra

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Book Summary:

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Directory of Published Proceedings

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Directory of Published Proceedings by N.A Book Summary:

Download or read Directory of Published Proceedings book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Combinatorial Aspect of Integrable Systems

Combinatorial Aspects Of Commutative Algebra [Pdf/ePub] eBook

Combinatorial Aspect of Integrable Systems by Arkady Berenstein,David Kazhdan,Cedric Lecouvey Book Summary:

This volume is a collection of six papers based on the expository lectures of the workshop "Combinatorial Aspect of Integrable Systems" held at RIMS during July 26-30, 2004, as a part of the Project Research 2004 "Method of Algebraic Analysis in Integrable Systems". The topics range over crystal bases of quantum groups, its algebra-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets