The Combinatorics Of Polynomial Sequences
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The Combinatorics Of Polynomial Sequences
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Author : David Lawrence Reiner
language : en
Publisher:
Release Date : 1975
The Combinatorics Of Polynomial Sequences written by David Lawrence Reiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
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.
Combinatorics And Number Theory Of Counting Sequences
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Author : Istvan Mezo
language : en
Publisher: CRC Press
Release Date : 2019-08-19
Combinatorics And Number Theory Of Counting Sequences written by Istvan Mezo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-19 with Computers categories.
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.
Unimodal Log Concave And Polya Frequency Sequences In Combinatorics
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Author : Francesco Brenti
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Unimodal Log Concave And Polya Frequency Sequences In Combinatorics written by Francesco Brenti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Many sequences of combinatorial interest are known to be unimodal or log-concave and there has been a considerable amount of interest devoted to this topic. The main object of this work is to point out another branch of mathematics that can be successfully used to attack these kinds of problems, namely, the theory of total positivity.
Polynomial Sequences
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Author : Francesco Aldo Costabile
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-12-18
Polynomial Sequences written by Francesco Aldo Costabile and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-18 with Mathematics categories.
Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.
Algebraic Combinatorics
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Author : Richard P. Stanley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-17
Algebraic Combinatorics written by Richard P. Stanley 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 2013-06-17 with Mathematics categories.
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Number Theory And Polynomials
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Author : James Fraser McKee
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-08
Number Theory And Polynomials written by James Fraser McKee 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 2008-05-08 with Mathematics categories.
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
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.
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
Combinatorics The Rota Way
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Author : Joseph P. S. Kung
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-09
Combinatorics The Rota Way written by Joseph P. S. Kung 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 2009-02-09 with Mathematics categories.
Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.