EXTREMAL FINITE SET THEORY (HB 2019) Hardcover

Extremal Finite Set Theory provides an in-depth exploration of both classical and modern results in extremal set system theory. The book highlights key techniques and tools used in the field, such as shifting, the cycle method, profile polytopes, incidence matrices, and flag algebras. It focuses on examining the cardinality of set families that adhere to specific combinatorial properties, exploring recent advancements in set systems and extremal combinatorics. Targeted at graduate students, instructors, and researchers in extremal combinatorics, this book offers a solid introduction to the theory of extremal set systems. Each chapter introduces the essential tools used in the literature and presents detailed proofs of the most important and recent results. Some proofs are left as exercises, accompanied by hints.