The Unity Of Combinatorics

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The Unity of Combinatorics

Ezra Brown,Richard K. Guy
The Unity of Combinatorics Book PDF

Author : Ezra Brown,Richard K. Guy
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 43,7 Mb
Release : 2021-04-05
Category : Education
ISBN : 9781470465094

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The Unity of Combinatorics by Ezra Brown,Richard K. Guy Pdf

Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

The Unity of Combinatorics

Ezra A. Brown,Richard K. Guy
The Unity of Combinatorics Book PDF

Author : Ezra A. Brown,Richard K. Guy
Publisher : MAA Press
Page : 128 pages
File Size : 41,5 Mb
Release : 2020
Category : Combinatorial analysis
ISBN : 1470456672

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The Unity of Combinatorics by Ezra A. Brown,Richard K. Guy Pdf

Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyo.

Combinatorics Advances

Charles J. Colbourn,Ebdollah Sayed Mahmoodian
Combinatorics Advances Book PDF

Author : Charles J. Colbourn,Ebdollah Sayed Mahmoodian
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 53,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461335542

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Combinatorics Advances by Charles J. Colbourn,Ebdollah Sayed Mahmoodian Pdf

On March 28~31, 1994 (Farvardin 8~11, 1373 by Iranian calendar), the Twenty fifth Annual Iranian Mathematics Conference (AIMC25) was held at Sharif University of Technology in Tehran, Islamic Republic of Iran. Its sponsors in~ eluded the Iranian Mathematical Society, and the Department of Mathematical Sciences at Sharif University of Technology. Among the keynote speakers were Professor Dr. Andreas Dress and Professor Richard K. Guy. Their plenary lec~ tures on combinatorial themes were complemented by invited and contributed lectures in a Combinatorics Session. This book is a collection of refereed papers, submitted primarily by the participants after the conference. The topics covered are diverse, spanning a wide range of combinatorics and al~ lied areas in discrete mathematics. Perhaps the strength and variety of the pa~ pers here serve as the best indications that combinatorics is advancing quickly, and that the Iranian mathematics community contains very active contributors. We hope that you find the papers mathematically stimulating, and look forward to a long and productive growth of combinatorial mathematics in Iran.

Combinatorics: The Art of Counting

Bruce E. Sagan
Combinatorics The Art of Counting Book PDF

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 46,7 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.

Combinatorics: Ancient & Modern

Robin Wilson,John J. Watkins
Combinatorics Ancient Modern Book PDF

Author : Robin Wilson,John J. Watkins
Publisher : OUP Oxford
Page : 392 pages
File Size : 42,8 Mb
Release : 2013-06-27
Category : Mathematics
ISBN : 9780191630620

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Combinatorics: Ancient & Modern by Robin Wilson,John J. Watkins Pdf

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Combinatorics: The Rota Way

Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan
Combinatorics The Rota Way Book PDF

Author : Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan
Publisher : Cambridge University Press
Page : 397 pages
File Size : 48,7 Mb
Release : 2009-02-09
Category : Mathematics
ISBN : 9781139476768

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Combinatorics: The Rota Way by Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan Pdf

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

Analytic Combinatorics in Several Variables

Robin Pemantle,Mark C. Wilson
Analytic Combinatorics in Several Variables Book PDF

Author : Robin Pemantle,Mark C. Wilson
Publisher : Cambridge University Press
Page : 395 pages
File Size : 55,6 Mb
Release : 2013-05-31
Category : Mathematics
ISBN : 9781107031579

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Analytic Combinatorics in Several Variables by Robin Pemantle,Mark C. Wilson Pdf

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.

Algebraic Combinatorics

Richard P. Stanley
Algebraic Combinatorics Book PDF

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 41,8 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.

Analytic Combinatorics

Philippe Flajolet,Robert Sedgewick
Analytic Combinatorics Book PDF

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 46,9 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.

The Surprising Mathematics of Longest Increasing Subsequences

Dan Romik
The Surprising Mathematics of Longest Increasing Subsequences Book PDF

Author : Dan Romik
Publisher : Cambridge University Press
Page : 366 pages
File Size : 51,6 Mb
Release : 2015-02-02
Category : Mathematics
ISBN : 9781107075832

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The Surprising Mathematics of Longest Increasing Subsequences by Dan Romik Pdf

This book presents for the first time to a graduate-level readership recent groundbreaking developments in probability and combinatorics related to the longest increasing subsequence problem. Its detailed, playful presentation provides a motivating entry to elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists, and statisticians.

102 Combinatorial Problems

Titu Andreescu,Zuming Feng
102 Combinatorial Problems Book PDF

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 48,6 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.

The Rise and Fall of the German Combinatorial Analysis

Eduardo Noble
The Rise and Fall of the German Combinatorial Analysis Book PDF

Author : Eduardo Noble
Publisher : Springer Nature
Page : 424 pages
File Size : 46,9 Mb
Release : 2022-05-30
Category : Mathematics
ISBN : 9783030938208

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The Rise and Fall of the German Combinatorial Analysis by Eduardo Noble Pdf

This text presents the ideas of a particular group of mathematicians of the late 18th century known as “the German combinatorial school” and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.

Introduction to Combinatorial Methods in Geometry

A. B. Kharazishvili
Introduction to Combinatorial Methods in Geometry Book PDF

Author : A. B. Kharazishvili
Publisher : Unknown
Page : 0 pages
File Size : 47,8 Mb
Release : 2024
Category : Mathematics
ISBN : 1032594705

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Introduction to Combinatorial Methods in Geometry by A. B. Kharazishvili Pdf

This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry. The author's primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc. All chapters (and also the five Appendixes) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints. The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.

Triple Systems

Charles J. Colbourn,Alexander Rosa
Triple Systems Book PDF

Author : Charles J. Colbourn,Alexander Rosa
Publisher : Oxford University Press
Page : 582 pages
File Size : 44,6 Mb
Release : 1999
Category : Computers
ISBN : 0198535767

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Triple Systems by Charles J. Colbourn,Alexander Rosa Pdf

Among the simplest combinatorial designs, triple systems have diverse applications in coding theory, cryptography, computer science, and statistics. This book provides a systematic and comprehensive treatment of this rich area of mathematics.

Representations of Hecke Algebras at Roots of Unity

Meinolf Geck,Nicolas Jacon
Representations of Hecke Algebras at Roots of Unity Book PDF

Author : Meinolf Geck,Nicolas Jacon
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 44,8 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9780857297167

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Representations of Hecke Algebras at Roots of Unity by Meinolf Geck,Nicolas Jacon Pdf

The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.