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Analytic Combinatorics in Several Variables

2013-05-31 Mathematics
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Release : 2013-05-31
Genre : Mathematics
Kind : eBook
Book Rating : 575/5 ( reviews)

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Book Synopsis Analytic Combinatorics in Several Variables by : Robin Pemantle

Download or read book Analytic Combinatorics in Several Variables written by Robin Pemantle. This book was released on 2013-05-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Invitation to Analytic Combinatorics

2020-12-22 Mathematics
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Release : 2020-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 805/5 ( reviews)

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Book Synopsis An Invitation to Analytic Combinatorics by : Stephen Melczer

Download or read book An Invitation to Analytic Combinatorics written by Stephen Melczer. This book was released on 2020-12-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2009-01-15 Mathematics
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Release : 2009-01-15
Genre : Mathematics
Kind : eBook
Book Rating : 161/5 ( reviews)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet. This book was released on 2009-01-15. Available in PDF, EPUB and Kindle. Book excerpt: 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 for Multiple Object Tracking

2020-11-26 Technology & Engineering
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Release : 2020-11-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 914/5 ( reviews)

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Book Synopsis Analytic Combinatorics for Multiple Object Tracking by : Roy Streit

Download or read book Analytic Combinatorics for Multiple Object Tracking written by Roy Streit. This book was released on 2020-11-26. Available in PDF, EPUB and Kindle. Book excerpt: ​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 in Several Variables

2024 MATHEMATICS
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Release : 2024
Genre : MATHEMATICS
Kind : eBook
Book Rating : 144/5 ( reviews)

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Book Synopsis Analytic Combinatorics in Several Variables by : Robin Pemantle

Download or read book Analytic Combinatorics in Several Variables written by Robin Pemantle. This book was released on 2024. Available in PDF, EPUB and Kindle. Book excerpt: "Discrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such structures"--

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