Arithmetic And Combinatorics

Author : Jiri Herman,Radan Kucera,Jaromir Simsa
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 52,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475739251

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Counting and Configurations by Jiri Herman,Radan Kucera,Jaromir Simsa Pdf

This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.

Author : Terence Tao,Van H. Vu
Publisher : Cambridge University Press
Page : 18 pages
File Size : 49,5 Mb
Release : 2006-09-14
Category : Mathematics
ISBN : 9781139458344

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Additive Combinatorics by Terence Tao,Van H. Vu Pdf

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 45,5 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470460327

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Combinatorics: The Art of Counting by Bruce E. Sagan Pdf

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 42,9 Mb
Release : 2013-06-17
Category : Mathematics
ISBN : 9781461469988

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Algebraic Combinatorics by Richard P. Stanley Pdf

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.

Author : Martin J. Erickson
Publisher : John Wiley & Sons
Page : 210 pages
File Size : 43,5 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118030899

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Introduction to Combinatorics by Martin J. Erickson Pdf

This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 50,8 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Author : George Polya,Robert E. Tarjan,Donald R. Woods
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 44,7 Mb
Release : 2013-11-27
Category : Science
ISBN : 9781475711011

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Notes on Introductory Combinatorics by George Polya,Robert E. Tarjan,Donald R. Woods Pdf

In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

Author : Chuan-Chong Chen,Khee Meng Koh,Koh Khee-Meng
Publisher : World Scientific
Page : 314 pages
File Size : 52,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9810211392

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Principles and Techniques in Combinatorics by Chuan-Chong Chen,Khee Meng Koh,Koh Khee-Meng Pdf

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Author : Nicholas Loehr
Publisher : CRC Press
Page : 600 pages
File Size : 52,5 Mb
Release : 2011-02-10
Category : Computers
ISBN : 9781439848869

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Bijective Combinatorics by Nicholas Loehr Pdf

Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9780817681548

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A Path to Combinatorics for Undergraduates by Titu Andreescu,Zuming Feng Pdf

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 44,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9780817682224

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102 Combinatorial Problems by Titu Andreescu,Zuming Feng Pdf

"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

Author : Anders Bjorner,Francesco Brenti
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 44,5 Mb
Release : 2006-02-25
Category : Mathematics
ISBN : 9783540275961

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Combinatorics of Coxeter Groups by Anders Bjorner,Francesco Brenti Pdf

Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 53,7 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

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.

Author : John Harris,Jeffry L. Hirst,Michael Mossinghoff
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 51,9 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387797113

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Combinatorics and Graph Theory by John Harris,Jeffry L. Hirst,Michael Mossinghoff Pdf

These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Author : W. D. Wallis,A. P. Street,J. S. Wallis
Publisher : Springer
Page : 503 pages
File Size : 51,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540379942

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Combinatorics by W. D. Wallis,A. P. Street,J. S. Wallis Pdf