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Extremal Finite Set Theory
— —
Daniel Gerbner Balazs Patkos
Extremal Finite Set Theory by Daniel Gerbner at Abbey's Bookshop,

Extremal Finite Set Theory

Daniel Gerbner Balazs Patkos


9781138197848

CRC Press


Combinatorics & graph theory


Hardback

336 pages

$122.00
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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:

Daniel Gerbner is a researcher at the Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.

D. from Eoetvoes Lorand University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory.

Balazs Patkos is also a researcher at the Alfred Renyi 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.

By:   Daniel Gerbner, Balazs Patkos
Imprint:   CRC Press
Country of Publication:   United Kingdom
Dimensions:   Height: 235mm,  Width: 156mm, 
Weight:   281g
ISBN:   9781138197848
ISBN 10:   113819784X
Series:   Discrete Mathematics and Its Applications
Pages:   336
Publication Date:   October 2018
Audience:   College/higher education ,  College/higher education ,  Primary ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active

Basics Sperner's theorem, LYM-inequality, Bollobas inequality. The Erdos-Ko-Rado theorem - several proofs. Intersecting Sperner families. Isoperimetric inequalities: the Kruskal-Katona theorem and Harper's theorem. Sunflowers. Intersection theorems Stability of the Erdos-Ko-Rado theorem. t-intersecting families. Above the Erdos-Ko-Rado threshold. L-intersecting families. r-wise intersecting families. k-uniform intersecting families with covering number k. The number of intersecting families. Cross-intersecting families. Sperner-type theorems More-part Sperner families. Supersaturation. The number of antichains in 2^{[n]} (Dedekind's problem). Union-free families and related problems. Union-closed families. Random versions of Sperner's theorem and the Erdos-Ko-Rado theorem The largest antichain in Qn (p). Largest intersecting families in Qn, k (p). Removing edges from K n (n, K). G-intersecting families. A random process generating intersecting families. Turan-type problems Complete forbidden hypergraphs and local sparsity. Graph-based forbidden hypergraphs. Hypergraph-based forbidden hypergraphs. Other forbidden hypergraphs. Some methods. Non-uniform Turan problems Saturation problems Saturated hypergraphs and weak saturation. Saturating k-Sperner families and related problems. Forbidden subposet problems Chain partitioning and other methods. General bounds on La(n, P) involving the height of P. Supersaturation. Induced forbidden subposet problems. Other variants of the problem. Counting other subposets. Traces of sets Characterizing the case of equality in the Sauer Lemma. The arrow relation. Forbidden subconfigurations. Uniform versions. Combinatorial search theory Basics. Searching with small query sets. Parity search. Searching with lies. Between adaptive and non-adaptive algorithms

Daniel Gerbner is a researcher at the Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eoetvoes Lorand University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balazs Patkos is also a researcher at the Alfred Renyi 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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