Gerbner D., Patkós B. Extremal Finite Set Theory

Boca Raton: CRC Press, 2018. — 351 p. — (Discrete Mathematics and Its Applications). — ISBN: 113819784X.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.Notation and Definitions.
Basics.
Intersection theorems.
Sperner-type theorems.
Random versions of Sperner’s theorem and the Erdos-Ko-Rado theorem.
Turan-type problems.
Saturation problems.
Forbidden subposet problems.
Traces of sets.
Combinatorial search theory.True PDF