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Analytic Combinatorics

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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.

Analytic Combinatorics

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Author : Marni Mishna
language : en
Publisher: CRC Press
Release Date : 2019-11-29

Analytic Combinatorics written by Marni Mishna and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-29 with Mathematics categories.

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.

An Invitation To Analytic Combinatorics

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Author : Stephen Melczer
language : en
Publisher: Springer Nature
Release Date : 2020-12-22

An Invitation To Analytic Combinatorics written by Stephen Melczer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with Mathematics categories.

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.

Analytic Combinatorics In Several Variables

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Author : Robin Pemantle
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-15

Analytic Combinatorics In Several Variables written by Robin Pemantle 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 2024-02-15 with Mathematics categories.

Introduces the theory of multivariate generating functions, with new exercises, computational examples, and a conceptual overview chapter.

Analytic Combinatorics For Multiple Object Tracking

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Author : Roy Streit
language : en
Publisher: Springer Nature
Release Date : 2020-11-26

Analytic Combinatorics For Multiple Object Tracking written by Roy Streit and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Technology & Engineering categories.

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.

Introduction To Enumerative And Analytic Combinatorics

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-09-18

Introduction To Enumerative And Analytic Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Computers categories.

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 enumerat

Introduction To Enumerative And Analytic Combinatorics

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2025-03-11

This award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author’s goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. 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. Updates to the Third Edition include: Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter. A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book. An extended section on multivariate generating functions. Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation. The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.

Analytic Combinatorics

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Author : Marni Mishna
language : en
Publisher: CRC Press
Release Date : 2019-11-27

Combinatorial Physics

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Author : Adrian Tanasa
language : en
Publisher: Oxford University Press
Release Date : 2021

Combinatorial Physics written by Adrian Tanasa and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Computers categories.

The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.

Handbook Of Enumerative Combinatorics

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-03-24

Handbook Of Enumerative Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.

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 Miklos Bona of the University of Florida where he

Analytic Combinatorics

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