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Author | : Peter Frankl |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2018-08-15 |
Genre | : Extremal problems |
ISBN | : 1470440393 |
Download Extremal Problems for Finite Sets Book 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.
Author | : Paulette Lieby |
Publisher | : |
Total Pages | : 238 |
Release | : 1999 |
Genre | : Set theory |
ISBN | : |
Download Extremal Problems in Finite Sets Book in PDF, ePub and Kindle
Author | : Moya Michelle Mazorow |
Publisher | : |
Total Pages | : 210 |
Release | : 1991 |
Genre | : Electronic dissertations |
ISBN | : |
Download Extremal Problems in Codes, Finite Sets and Geometries Book in PDF, ePub and Kindle
Author | : Daniel Gerbner |
Publisher | : CRC Press |
Total Pages | : 269 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 0429804113 |
Download Extremal Finite Set Theory Book 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.
Author | : Ian Anderson |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780486422572 |
Download Combinatorics of Finite Sets Book 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.
Author | : A.G. Chentsov |
Publisher | : Springer Science & Business Media |
Total Pages | : 261 |
Release | : 1996-09-30 |
Genre | : Language Arts & Disciplines |
ISBN | : 0306110385 |
Download Finitely Additive Measures and Relaxations of Extremal Problems Book in PDF, ePub and Kindle
This monograph constructs correct extensions of extremal problems, including problems of multicriteria optimization as well as more general cone optimization problems. The author obtains common conditions of stability and asymptotic nonsensitivity of extremal problems under perturbation of a part of integral restrictions for finite and infinite systems of restrictions. Features include individual chapters on nonstandard approximation of finitely additive measures by indefinite integrals and constructions of attraction sets. Professor Chentsov illustrates abstract settings by providing examples of problems of impulse control, mathematical programming, and stochastic optimization.
Author | : Attila Sali |
Publisher | : |
Total Pages | : 226 |
Release | : 1986 |
Genre | : Extremal problems (Mathematics) |
ISBN | : |
Download Extremal Problems for Finite Partially Ordered Sets Book in PDF, ePub and Kindle
Author | : Benjamin Lund |
Publisher | : |
Total Pages | : 93 |
Release | : 2017 |
Genre | : Discrete geometry |
ISBN | : |
Download Incidences and Extremal Problems on Finite Point Sets Book in PDF, ePub and Kindle
This thesis consists of three papers, each addressing a different collection of problems on the extremal combinatorics of finite point sets. The first collection of results is on the number of flats of each dimensions spanned by a set of points in $mathbb{R}^d$. These results generalize a theorem of Beck cite{beck1983lattice} from 1983, and answer a question of Purdy cite{erdos1996extremal} from 1995. We also apply the ideas behind the main results of the chapter to generalize an incidence bound between points and planes proved by Elekes and T'oth cite{elekes2005incidences} to all dimensions. With the exception of the generalization of the Elekes-T'oth incidence bound, all of the material in this chapter has previously appeared as cite{lund2016essential}. The second collection of results is on the set of perpendicular bisectors determined by a set of points in the plane. We show that if $P$ is a set of points in $mathbb{R}^2$ such that no line or circle contains more than a large constant fraction of the points of $P$, the the pairs of points of $P$ determine a substantially superlinear number of distinct perpendicular bisectors. This is the first substantial progress toward a conjecture of the author, Sheffer, and de Zeeuw cite{lund2015bisector} that such a set of points must determine $Omega(n^2)$ distinct perpendicular bisectors. This chapter also includes a new proof of a known result on an old question ErdH{o}s cite{erdos1946sets} on the distances between pairs of points in the plane. This chapter is cite{lund2016refined}. The third collection of results concerns the set of flats spanned by a set of points in $mathbb{F}_q^d$. For a set of points $P$ in $mathbb{F}_q^2$, this result implies that, for any $eps> 0$, if $
Author | : Ian Thomas Roberts |
Publisher | : |
Total Pages | : 352 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Extremal Problems and Designs on Finite Sets Book in PDF, ePub and Kindle
A flat antichain is an antichain in which the difference in cardinality between any two sets in the antichain is at most one. The two outstanding conjectures considered are: The union-closed sets conjecture - In any union-closed collection of non-empty sets there is an element of the universal set in at least half of the sets in the collection; The flat antichain conjecture - Given an antichain with size s and volume V, there is a flat antichain with the same size and volume. Union-closed collections are considered in two ways. Improvements are made to the previously known bounds concerning the minimum size of a counterexample to the union-closed sets conjecture.
Author | : Stanislav V. Emelyanov |
Publisher | : Walter de Gruyter |
Total Pages | : 317 |
Release | : 2011-12-22 |
Genre | : Mathematics |
ISBN | : 3110893010 |
Download Homotopy of Extremal Problems Book in PDF, ePub and Kindle
This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. Thorough treatment of parameter-dependent extremal problems with local minimum values. Includes many applications, e.g., variational calculus, control theory and bifurcations theory. Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects.