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Combinatorics of Finite Sets

2012-04-30 Mathematics
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Release : 2012-04-30
Genre : Mathematics
Kind : eBook
Book Rating : 716/5 ( reviews)

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Book Synopsis Combinatorics of Finite Sets by : Ian Anderson

Download or read book Combinatorics of Finite Sets written by Ian Anderson. This book was released on 2012-04-30. Available in PDF, EPUB and Kindle. Book excerpt: Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics." — Bulletin of the American Mathematical Society.

Combinatorics of Finite Sets

2002-01-01 Mathematics
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Release : 2002-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 572/5 ( reviews)

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Book Synopsis Combinatorics of Finite Sets by : Ian Anderson

Download or read book Combinatorics of Finite Sets written by Ian Anderson. This book was released on 2002-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

1987 Art
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Release : 1987
Genre : Art
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Combinatorics of Finite Sets by : Ian Anderson (Ph. D.)

Download or read book Combinatorics of Finite Sets written by Ian Anderson (Ph. D.). This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt: 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

2018-08-15 Mathematics
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Release : 2018-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 393/5 ( reviews)

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Book Synopsis Extremal Problems for Finite Sets by : Peter Frankl

Download or read book Extremal Problems for Finite Sets written by Peter Frankl. This book was released on 2018-08-15. Available in PDF, EPUB and Kindle. Book excerpt: 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

2018-10-12 Mathematics
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Release : 2018-10-12
Genre : Mathematics
Kind : eBook
Book Rating : 113/5 ( reviews)

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Book Synopsis Extremal Finite Set Theory by : Daniel Gerbner

Download or read book Extremal Finite Set Theory written by Daniel Gerbner. This book was released on 2018-10-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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