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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
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.

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 An Invitation to Analytic 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 for Multiple Object Tracking
Author Roy Streit
Publisher Springer Nature
Release 2020-11-26
Category Technology & Engineering
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 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.

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 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.

Analytic Pattern Matching by Philippe Jacquet

Title Analytic Pattern Matching
Author Philippe Jacquet
Publisher Cambridge University Press
Release 2015-06-30
Category Computers
Total Pages
ISBN 1316298043
Language English, Spanish, and French
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Book Summary:

How do you distinguish a cat from a dog by their DNA? Did Shakespeare really write all of his plays? Pattern matching techniques can offer answers to these questions and to many others, from molecular biology, to telecommunications, to classifying Twitter content. This book for researchers and graduate students demonstrates the probabilistic approach to pattern matching, which predicts the performance of pattern matching algorithms with very high precision using analytic combinatorics and analytic information theory. Part I compiles known results of pattern matching problems via analytic methods. Part II focuses on applications to various data structures on words, such as digital trees, suffix trees, string complexity and string-based data compression. The authors use results and techniques from Part I and also introduce new methodology such as the Mellin transform and analytic depoissonization. More than 100 end-of-chapter problems help the reader to make the link between theory and practice.

Title Algorithmic Probability and Combinatorics
Author Manuel Lladser
Publisher American Mathematical Soc.
Release 2010-07-30
Category Mathematics
Total Pages 240
ISBN 082184783X
Language English, Spanish, and French
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Book Summary:

This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.

Title Handbook of Enumerative Combinatorics
Author Miklos Bona
Publisher CRC Press
Release 2015-03-24
Category Mathematics
Total Pages 1086
ISBN 1482220865
Language English, Spanish, and French
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Book Summary:

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

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