Analytic Combinatorics
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Analytic Combinatorics In Several Variables
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Author : Robin Pemantle
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-31
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 2013-05-31 with Mathematics categories.
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.
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.
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.
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 Second Edition
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Author : Miklos Bona
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2015-10-16
Introduction To Enumerative And Analytic Combinatorics Second Edition written by Miklos Bona and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-16 with Computers categories.
Divided into three parts, this book fills in the gap between introductory texts in discrete mathematics and advanced graduate textbooks in enumerative combinatorics. Part I deals with basic counting principles, compositions and partitions, and generating functions. Part II focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Finally, Part III covers supplemental topics, including error-correcting codes, properties of sequences, and magic squares.
Combinatorics Words And Symbolic Dynamics
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Author : Valérie Berthé
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-26
Combinatorics Words And Symbolic Dynamics written by Valérie Berthé 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 2016-02-26 with Computers categories.
Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science.
Combinatorics And Graph Theory
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Author : John Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Combinatorics And Graph Theory written by John Harris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.