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Analytic Combinatorics by Philippe Flajolet

Title Analytic Combinatorics
Author Philippe Flajolet
Publisher Cambridge University Press
Release 2009-01-15
Category Mathematics
Total Pages 826
ISBN 9780521898065
Language English, Spanish, and French
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Book Summary:

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Title Introduction to Enumerative and Analytic Combinatorics
Author Miklos Bona
Publisher CRC Press
Release 2015-09-18
Category Computers
Total Pages 534
ISBN 1482249103
Language English, Spanish, and French
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Book Summary:

Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, this Second Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field. Outstanding Academic Title of the Year, Choice magazine, American Library Association.

Analytic Combinatorics by Marni Mishna

Title Analytic Combinatorics
Author Marni Mishna
Publisher CRC Press
Release 2019-11-27
Category Mathematics
Total Pages 230
ISBN 1351036815
Language English, Spanish, and French
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Book Summary:

Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory. The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry. Features Written with combinatorics-centric exposition to illustrate advanced analytic techniques Each chapter includes problems, exercises, and reviews of the material discussed in them Includes a comprehensive glossary, as well as lists of figures and symbols About the author Marni Mishna is a professor of mathematics at Simon Fraser University in British Columbia. Her research investigates interactions between discrete structures and many diverse areas such as representation theory, functional equation theory, and algebraic geometry. Her specialty is the development of analytic tools to study the large-scale behavior of discrete objects.

Title Analytic Combinatorics for Multiple Object Tracking
Author Roy Streit
Publisher Springer
Release 2020-11-27
Category Technology & Engineering
Total Pages 221
ISBN 9783030611903
Language English, Spanish, and French
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Book Summary:

​The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking—without information loss—into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book.

Analytic Combinatorics by Philippe Flajolet

Title Analytic Combinatorics
Author Philippe Flajolet
Publisher Cambridge University Press
Release 2009-01-15
Category Mathematics
Total Pages
ISBN 1139477161
Language English, Spanish, and French
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Book Summary:

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.

Title Algorithmic and Symbolic Combinatorics
Author Stephen Melczer
Publisher Springer Nature
Release 2020-12-22
Category Mathematics
Total Pages 418
ISBN 3030670805
Language English, Spanish, and French
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Book Summary:

This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

Title Analytic Combinatorics in Several Variables
Author Robin Pemantle
Publisher Cambridge University Press
Release 2013-05-31
Category Mathematics
Total Pages 380
ISBN 1107031575
Language English, Spanish, and French
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Book Summary:

This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.

Analytic Combinatorics by Marni Mishna

Title Analytic Combinatorics
Author Marni Mishna
Publisher CRC Press
Release 2019-11-29
Category Mathematics
Total Pages 230
ISBN 1351036807
Language English, Spanish, and French
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Book Summary:

Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory. The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry. Features Written with combinatorics-centric exposition to illustrate advanced analytic techniques Each chapter includes problems, exercises, and reviews of the material discussed in them Includes a comprehensive glossary, as well as lists of figures and symbols About the author Marni Mishna is a professor of mathematics at Simon Fraser University in British Columbia. Her research investigates interactions between discrete structures and many diverse areas such as representation theory, functional equation theory, and algebraic geometry. Her specialty is the development of analytic tools to study the large-scale behavior of discrete objects.

Title Analytic Combinatorics for Multiple Object Tracking
Author Roy Streit
Publisher Springer Nature
Release 2020
Category Combinatorial analysis
Total Pages 221
ISBN 3030611914
Language English, Spanish, and French
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Book Summary:

The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking--without information loss--into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book.

Title An Introduction to the Analysis of Algorithms
Author Robert Sedgewick
Publisher Addison-Wesley
Release 2013-01-18
Category Computers
Total Pages 604
ISBN 0133373487
Language English, Spanish, and French
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Book Summary:

Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field. Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance. Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure. Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s The Art of Computer Programming books—and provide the background they need to keep abreast of new research. "[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways." —From the Foreword by Donald E. Knuth

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