Combinatorics And Complexity Of Partition Functions
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Combinatorics And Complexity Of Partition Functions
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Author : Alexander Barvinok
language : en
Publisher: Springer
Release Date : 2017-03-13
Combinatorics And Complexity Of Partition Functions written by Alexander Barvinok and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-13 with Mathematics categories.
Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.
Model Theoretic Methods In Finite Combinatorics
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Author : Martin Grohe
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-11-28
Model Theoretic Methods In Finite Combinatorics written by Martin Grohe 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 2011-11-28 with Mathematics categories.
This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC. Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics. This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.
Surveys In Combinatorics 2024
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Author : Felix Fischer
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-13
Surveys In Combinatorics 2024 written by Felix Fischer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-13 with Mathematics categories.
This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, held at Queen Mary University of London in July 2024. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include: Latin squares, Erdős covering systems, finite field models, sublinear expanders, cluster expansion, the slice rank polynomial method, and oriented trees and paths in digraphs. The authors are among the world's foremost researchers on their respective topics but their surveys are accessible to nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, helping researchers and graduate students in mathematics and theoretical computer science to keep abreast of the latest developments in the field.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-15 with Mathematics categories.
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
A Course In Convexity
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Author : Alexander Barvinok
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-11-19
A Course In Convexity written by Alexander Barvinok 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 2002-11-19 with Mathematics categories.
Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.
Computing And Combinatorics
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Author : Bin Fu
language : en
Publisher: Springer
Release Date : 2011-07-18
Computing And Combinatorics written by Bin Fu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Computers categories.
This book constitutes the refereed proceedings of the 17th Annual International Conference on Computing and Combinatorics, held in Dallas, TX, USA, in August 2011. The 54 revised full papers presented were carefully reviewed and selected from 136 submissions. Topics covered are algorithms and data structures; algorithmic game theory and online algorithms; automata, languages, logic, and computability; combinatorics related to algorithms and complexity; complexity theory; computational learning theory and knowledge discovery; cryptography, reliability and security, and database theory; computational biology and bioinformatics; computational algebra, geometry, and number theory; graph drawing and information visualization; graph theory, communication networks, and optimization; parallel and distributed computing.
Extended Abstracts Eurocomb 2021
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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Nature
Release Date : 2021-08-23
Extended Abstracts Eurocomb 2021 written by Jaroslav Nešetřil and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-23 with Mathematics categories.
This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.
Open Problems In Algebraic Combinatorics
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Author : Christine Berkesch
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-21
Open Problems In Algebraic Combinatorics written by Christine Berkesch and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Recent Trends In Combinatorics
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Author : Andrew Beveridge
language : en
Publisher: Springer
Release Date : 2016-04-12
Recent Trends In Combinatorics written by Andrew Beveridge and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-12 with Mathematics categories.
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.
Proceedings Of The 12th Asian Logic Conference
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Author : Rodney G Downey
language : en
Publisher: World Scientific
Release Date : 2013-05-07
Proceedings Of The 12th Asian Logic Conference written by Rodney G Downey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-07 with Mathematics categories.
The Asian Logic Conference is the most significant logic meeting outside of North America and Europe, and this volume represents work presented at, and arising from the 12th meeting. It collects a number of interesting papers from experts in the field. It covers many areas of logic.