Advances In Combinatorics

Author : Rudolf Ahlswede,Vladimir Blinovsky
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 42,7 Mb
Release : 2008-05-17
Category : Mathematics
ISBN : 9783540786023

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Lectures on Advances in Combinatorics by Rudolf Ahlswede,Vladimir Blinovsky Pdf

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

Author : Louis Comtet
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401021968

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Advanced Combinatorics by Louis Comtet Pdf

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Author : Ilias S. Kotsireas,Eugene V. Zima
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 55,8 Mb
Release : 2013-08-04
Category : Mathematics
ISBN : 9783642309793

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Advances in Combinatorics by Ilias S. Kotsireas,Eugene V. Zima Pdf

This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life.

Author : Charles J. Colbourn,Ebdollah Sayed Mahmoodian
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 52,6 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.

Author : Bruce A. Reed,Claudia L. Linhares-Sales
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 46,6 Mb
Release : 2006-05-17
Category : Mathematics
ISBN : 9780387224442

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Recent Advances in Algorithms and Combinatorics by Bruce A. Reed,Claudia L. Linhares-Sales Pdf

Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241409

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Advances in Combinatorial Methods and Applications to Probability and Statistics by N. Balakrishnan Pdf

Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.

Author : Bruce A. Reed
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 55,8 Mb
Release : 2003
Category : Business & Economics
ISBN : 9780387954349

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Recent Advances in Algorithms and Combinatorics by Bruce A. Reed Pdf

Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

Author : K. P. Shum
Publisher : World Scientific
Page : 384 pages
File Size : 55,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812790002

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Advances in Algebra and Combinatorics by K. P. Shum Pdf

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 45,6 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 : K. P. Shum
Publisher : World Scientific
Page : 384 pages
File Size : 54,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812790019

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Advances in Algebra and Combinatorics - Proceedings of the Second International Congress in Algebra and Combinatorics by K. P. Shum Pdf

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,8 Mb
Release : 2024-07-04
Category : Electronic
ISBN : 9789814472135

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Advances in Algebra and Combinatorics by Anonim Pdf

Author : Jiri Herman,Radan Kucera,Jaromir Simsa
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 41,9 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 : Martin J. Erickson
Publisher : John Wiley & Sons
Page : 210 pages
File Size : 45,8 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 : Ezra Brown,Richard K. Guy
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 46,6 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.”

Author : Robin Wilson,John J. Watkins
Publisher : OUP Oxford
Page : 392 pages
File Size : 48,7 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.