Current Trends On Monomial And Binomial Ideals

Author : Huy Tài Hà,Takayuki Hibi
Publisher : MDPI
Page : 140 pages
File Size : 53,6 Mb
Release : 2020-03-18
Category : Mathematics
ISBN : 9783039283606

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Current Trends on Monomial and Binomial Ideals by Huy Tài Hà,Takayuki Hibi Pdf

Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commutative algebra. The last ten years have seen a surge of research work in the study of monomial and binomial ideals. Remarkable developments in, for example, finite free resolutions, syzygies, Hilbert functions, toric rings, as well as cohomological invariants of ordinary powers, and symbolic powers of monomial and binomial ideals, have been brought forward. The theory of monomial and binomial ideals has many benefits from combinatorics and Göbner bases. Simultaneously, monomial and binomial ideals have created new and exciting aspects of combinatorics and Göbner bases. In the present Special Issue, particular attention was paid to monomial and binomial ideals arising from combinatorial objects including finite graphs, simplicial complexes, lattice polytopes, and finite partially ordered sets, because there is a rich and intimate relationship between algebraic properties and invariants of these classes of ideals and the combinatorial structures of their combinatorial counterparts. This volume gives a brief summary of recent achievements in this area of research. It will stimulate further research that encourages breakthroughs in the theory of monomial and binomial ideals. This volume provides graduate students with fundamental materials in this research area. Furthermore, it will help researchers find exciting activities and avenues for further exploration of monomial and binomial ideals. The editors express our thanks to the contributors to the Special Issue. Funds for APC (article processing charge) were partially supported by JSPS (Japan Society for the Promotion of Science) Grants-in-Aid for Scientific Research (S) entitled "The Birth of Modern Trends on Commutative Algebra and Convex Polytopes with Statistical and Computational Strategies" (JP 26220701). The publication of this volume is one of the main activities of the grant.

Author : Takayuki Hibi
Publisher : Unknown
Page : 140 pages
File Size : 43,5 Mb
Release : 2020
Category : Mathematics
ISBN : 3039283618

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Current Trends on Monomial and Binomial Ideals by Takayuki Hibi Pdf

Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commutative algebra. The last ten years have seen a surge of research work in the study of monomial and binomial ideals. Remarkable developments in, for example, finite free resolutions, syzygies, Hilbert functions, toric rings, as well as cohomological invariants of ordinary powers, and symbolic powers of monomial and binomial ideals, have been brought forward. The theory of monomial and binomial ideals has many benefits from combinatorics and Göbner bases. Simultaneously, monomial and binomial ideals have created new and exciting aspects of combinatorics and Göbner bases. In the present Special Issue, particular attention was paid to monomial and binomial ideals arising from combinatorial objects including finite graphs, simplicial complexes, lattice polytopes, and finite partially ordered sets, because there is a rich and intimate relationship between algebraic properties and invariants of these classes of ideals and the combinatorial structures of their combinatorial counterparts. This volume gives a brief summary of recent achievements in this area of research. It will stimulate further research that encourages breakthroughs in the theory of monomial and binomial ideals. This volume provides graduate students with fundamental materials in this research area. Furthermore, it will help researchers find exciting activities and avenues for further exploration of monomial and binomial ideals. The editors express our thanks to the contributors to the Special Issue. Funds for APC (article processing charge) were partially supported by JSPS (Japan Society for the Promotion of Science) Grants-in-Aid for Scientific Research (S) entitled ""The Birth of Modern Trends on Commutative Algebra and Convex Polytopes with Statistical and Computational Strategies"" (JP 26220701). The publication of this volume is one of the main activities of the grant.

Author : Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi
Publisher : Springer
Page : 321 pages
File Size : 53,9 Mb
Release : 2018-09-28
Category : Mathematics
ISBN : 9783319953496

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Binomial Ideals by Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi Pdf

This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. 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 statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource.

Author : Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 43,6 Mb
Release : 2016-12-08
Category : Combinatorial analysis
ISBN : 9781470427245

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The Mathematical Legacy of Richard P. Stanley by Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner Pdf

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.

Author : Jürgen Herzog,Takayuki Hibi
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 46,5 Mb
Release : 2010-09-28
Category : Mathematics
ISBN : 9780857291066

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Monomial Ideals by Jürgen Herzog,Takayuki Hibi Pdf

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.

Author : David A. Cox,John B. Little,Henry K. Schenck
Publisher : American Mathematical Soc.
Page : 874 pages
File Size : 52,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821848197

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Toric Varieties by David A. Cox,John B. Little,Henry K. Schenck Pdf

Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.

Author : Gert-Martin Greuel,Gerhard Pfister
Publisher : Springer Science & Business Media
Page : 703 pages
File Size : 47,8 Mb
Release : 2007-11-05
Category : Mathematics
ISBN : 9783540735410

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A Singular Introduction to Commutative Algebra by Gert-Martin Greuel,Gerhard Pfister Pdf

This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Author : José Luis Cisneros Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 616 pages
File Size : 45,8 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030530617

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Handbook of Geometry and Topology of Singularities I by José Luis Cisneros Molina,Dũng Tráng Lê,José Seade Pdf

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Author : Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels
Publisher : Cambridge University Press
Page : 7 pages
File Size : 46,5 Mb
Release : 2004-12-13
Category : Mathematics
ISBN : 9780521831956

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Trends in Commutative Algebra by Luchezar L. Avramov,Mark Green,Craig Huneke,Karen E. Smith,Bernd Sturmfels Pdf

This book describes the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology, and combinatorics.

Author : Jessica S. Sidman
Publisher : Unknown
Page : 170 pages
File Size : 51,5 Mb
Release : 2002
Category : Electronic
ISBN : UOM:39015055440138

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On the Castelnuovo-Mumford Regularity of Subspace Arrangements by Jessica S. Sidman Pdf

Author : Teo Mora
Publisher : Cambridge University Press
Page : 792 pages
File Size : 48,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0521811562

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Solving Polynomial Equation Systems II by Teo Mora Pdf

This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.

Author : Taekyun Kim
Publisher : MDPI
Page : 206 pages
File Size : 49,8 Mb
Release : 2021-03-19
Category : Mathematics
ISBN : 9783036503608

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Current Trends in Symmetric Polynomials with Their Applications Ⅱ by Taekyun Kim Pdf

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Author : Alicia Dickenstein,Ioannis Z. Emiris
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 47,7 Mb
Release : 2005-12-29
Category : Mathematics
ISBN : 9783540273578

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Solving Polynomial Equations by Alicia Dickenstein,Ioannis Z. Emiris Pdf

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Author : Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 45,5 Mb
Release : 2015-09-28
Category : Number theory
ISBN : 9780821898581

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Trends in Number Theory by Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero Pdf

This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Author : Anonim
Publisher : Unknown
Page : 1518 pages
File Size : 48,8 Mb
Release : 2005
Category : Mathematics
ISBN : UVA:X006195256

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Mathematical Reviews by Anonim Pdf