Combinatorics And Commutative Algebra

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Combinatorics and Commutative Algebra

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 49,9 Mb
Release : 2007-12-13
Category : Mathematics
ISBN : 9780817644338

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Combinatorics and Commutative Algebra by Richard P. Stanley Pdf

* 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

Combinatorial Commutative Algebra

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 40,8 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

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

Algebraic Combinatorics

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 48,8 Mb
Release : 2013-06-17
Category : Mathematics
ISBN : 9781461469988

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Algebraic Combinatorics by Richard P. Stanley Pdf

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.

Algebraic Combinatorics and Coinvariant Spaces

Author : Francois Bergeron
Publisher : CRC Press
Page : 230 pages
File Size : 53,8 Mb
Release : 2009-07-06
Category : Mathematics
ISBN : 9781439865071

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Algebraic Combinatorics and Coinvariant Spaces by Francois Bergeron Pdf

Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and some commutative algebra, the main material provides links between the study of coinvariant—or diagonally coinvariant—spaces and the study of Macdonald polynomials and related operators. This gives rise to a large number of combinatorial questions relating to objects counted by familiar numbers such as the factorials, Catalan numbers, and the number of Cayley trees or parking functions. The author offers ideas for extending the theory to other families of finite Coxeter groups, besides permutation groups.

Progress in Commutative Algebra 1

Author : Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 44,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110250404

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

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.

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Author : Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 40,5 Mb
Release : 2011-05-16
Category : Mathematics
ISBN : 9783642194924

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

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.

Computations and Combinatorics in Commutative Algebra

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 127 pages
File Size : 47,7 Mb
Release : 2017-03-14
Category : Mathematics
ISBN : 9783319513195

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

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.

Connections Between Algebra, Combinatorics, and Geometry

Author : Susan M. Cooper,Sean Sather-Wagstaff
Publisher : Springer
Page : 317 pages
File Size : 45,9 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9781493906260

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Connections Between Algebra, Combinatorics, and Geometry by Susan M. Cooper,Sean Sather-Wagstaff Pdf

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Introduction to Commutative Algebra and Algebraic Geometry

Author : Ernst Kunz
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 48,6 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459873

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Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz Pdf

Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Combinatorial Structures in Algebra and Geometry

Author : Dumitru I. Stamate,Tomasz Szemberg
Publisher : Springer Nature
Page : 182 pages
File Size : 54,8 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030521110

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Combinatorial Structures in Algebra and Geometry by Dumitru I. Stamate,Tomasz Szemberg Pdf

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).

Geometric And Combinatorial Aspects Of Commutative Algebra

Author : Jurgen Herzog,Gaetana Restuccia
Publisher : CRC Press
Page : 424 pages
File Size : 55,5 Mb
Release : 2001-03-06
Category : Mathematics
ISBN : 0203908015

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Geometric And Combinatorial Aspects Of Commutative Algebra by Jurgen Herzog,Gaetana Restuccia Pdf

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

Combinatorics and Commutative Algebra

Author : Richard Stanley
Publisher : Birkhäuser
Page : 168 pages
File Size : 41,9 Mb
Release : 1996-03-01
Category : Mathematics
ISBN : 0817638369

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Combinatorics and Commutative Algebra by Richard Stanley Pdf

* 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

Combinatorial Aspects of Commutative Algebra

Author : Viviana Ene,Ezra Miller
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 47,5 Mb
Release : 2009-11-25
Category : Mathematics
ISBN : 9780821847589

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Combinatorial Aspects of Commutative Algebra by Viviana Ene,Ezra Miller Pdf

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.

Constructive Commutative Algebra

Author : Ihsen Yengui
Publisher : Springer
Page : 277 pages
File Size : 49,9 Mb
Release : 2015-12-11
Category : Mathematics
ISBN : 9783319194943

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Constructive Commutative Algebra by Ihsen Yengui Pdf

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.

Combinatorial Set Theory of C*-algebras

Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 43,9 Mb
Release : 2019-12-24
Category : Mathematics
ISBN : 9783030270933

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Combinatorial Set Theory of C*-algebras by Ilijas Farah Pdf

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.