Sperner Theory
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Sperner Theory
Author | : Konrad Engel |
Publsiher | : Cambridge University Press |
Total Pages | : 430 |
Release | : 1997-01-28 |
Genre | : Mathematics |
ISBN | : 9780521452069 |
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The starting point of this book is Sperner's theorem, which answers the question: What is the maximum possible size of a family of pairwise (with respect to inclusion) subsets of a finite set? This theorem stimulated the development of a fast growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics. Researchers and graduate students in discrete mathematics, optimisation, algebra, probability theory, number theory, and geometry will find many powerful new methods arising from Sperner theory.
Extremal Finite Set Theory
Author | : Daniel Gerbner,Balazs Patkos |
Publsiher | : CRC Press |
Total Pages | : 269 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 9780429804113 |
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Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.
The Dilworth Theorems
Author | : Bogart,Kung,Freese |
Publsiher | : Springer Science & Business Media |
Total Pages | : 476 |
Release | : 2013-11-22 |
Genre | : Science |
ISBN | : 9781489935588 |
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Combinatorics The Rota Way
Author | : Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan |
Publsiher | : Cambridge University Press |
Total Pages | : 409 |
Release | : 2009-02-09 |
Genre | : Mathematics |
ISBN | : 9780521883894 |
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Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.
Development Of Mathematics Between The World Wars The Case Studies Examples And Analyses
Author | : Martina Becvarova |
Publsiher | : World Scientific |
Total Pages | : 623 |
Release | : 2021-05-14 |
Genre | : Mathematics |
ISBN | : 9781786349323 |
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The Development of Mathematics Between the World Wars traces the transformation of scientific life within mathematical communities during the interwar period in Central and Eastern Europe, specifically in Germany, Russia, Poland, Hungary, and Czechoslovakia. Throughout the book, in-depth mathematical analyses and examples are included for the benefit of the reader.World War I heavily affected academic life. In European countries, many talented researchers and students were killed in action and scientific activities were halted to resume only in the postwar years. However, this inhibition turned out to be a catalyst for the birth of a new generation of mathematicians, for the emergence of new ideas and theories and for the surprising creation of new and outstanding scientific schools.The final four chapters are not restricted to Central and Eastern Europe and deal with the development of mathematics between World War I and World War II. After describing the general state of mathematics at the end of the 19th century and the first third of the 20th century, three case studies dealing with selected mathematical disciplines are presented (set theory, potential theory, combinatorics), in a way accessible to a broad audience of mathematicians as well as historians of mathematics.
Orders Description and Roles
Author | : M. Pouzet,D. Richard |
Publsiher | : Elsevier |
Total Pages | : 547 |
Release | : 1984-01-01 |
Genre | : Mathematics |
ISBN | : 0080872107 |
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Orders: Description and Roles
Encyclopaedia of Mathematics Supplement III
Author | : Michiel Hazewinkel |
Publsiher | : Springer Science & Business Media |
Total Pages | : 564 |
Release | : 2007-11-23 |
Genre | : Mathematics |
ISBN | : 9780306483738 |
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This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Combinatorics Ancient Modern
Author | : Robin Wilson,John J. Watkins |
Publsiher | : OUP Oxford |
Total Pages | : 392 |
Release | : 2013-06-27 |
Genre | : Mathematics |
ISBN | : 9780191630620 |
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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.