Combinatorics of Finite Sets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combinatorics of Finite Sets write by Ian Anderson. This book was released on 2002-01-01. Combinatorics of Finite Sets available in PDF, EPUB and Kindle. Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
Combinatorics of Finite Sets
Combinatorics of Finite Sets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combinatorics of Finite Sets write by Ian Anderson (Ph. D.). This book was released on 1987. Combinatorics of Finite Sets available in PDF, EPUB and Kindle. It is the aim of this book to provide a coherent and up-to-date account of the basic methods and results of the combinatorial study of finite set systems.
Extremal Problems for Finite Sets
Extremal Problems for Finite Sets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Extremal Problems for Finite Sets write by Peter Frankl. This book was released on 2018-08-15. Extremal Problems for Finite Sets available in PDF, EPUB and Kindle. One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study. The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede-Khachatrian theorem as well as some recent progress on the Erdos matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza-Erdos-Frankl theorem, application of Rodl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdos-Szemeredi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
Extremal Finite Set Theory
Extremal Finite Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Extremal Finite Set Theory write by Daniel Gerbner. This book was released on 2018-10-12. Extremal Finite Set Theory available in PDF, EPUB and Kindle. 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.
Hypergraphs
Hypergraphs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hypergraphs write by C. Berge. This book was released on 1984-05-01. Hypergraphs available in PDF, EPUB and Kindle. Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.
