Combinatorics, Geometry and Probability
Author: Béla Bollobás
Publisher: Cambridge University Press
Published: 1997-05-22
Total Pages: 588
ISBN-13: 9780521584722
DOWNLOAD EBOOKA panorama of combinatorics by the world's experts.
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Combinatorics and Finite Geometry
Author: Steven T. Dougherty
Publisher: Springer Nature
Published: 2020-10-30
Total Pages: 374
ISBN-13: 3030563952
DOWNLOAD EBOOKThis undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
Random Trees
Author: Michael Drmota
Publisher: Springer Science & Business Media
Published: 2009-04-16
Total Pages: 466
ISBN-13: 3211753575
DOWNLOAD EBOOKThe aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.
Introduction to Geometric Probability
Author: Daniel A. Klain
Publisher: Cambridge University Press
Published: 1997-12-11
Total Pages: 196
ISBN-13: 9780521596541
DOWNLOAD EBOOKThe purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
Geometric Graphs and Arrangements
Author: Stefan Felsner
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 179
ISBN-13: 3322803031
DOWNLOAD EBOOKAmong the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Combinatorics and Probability
Author: Graham Brightwell
Publisher: Cambridge University Press
Published: 2007-03-08
Total Pages: 27
ISBN-13: 0521872073
DOWNLOAD EBOOKThis volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.
Combinatorics and Finite Geometry
Author: Steven T. Dougherty
Publisher: Springer
Published: 2020-10-31
Total Pages: 369
ISBN-13: 9783030563943
DOWNLOAD EBOOKThis undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
Combinatorics
Author: Béla Bollobás
Publisher: Cambridge University Press
Published: 1986-07-31
Total Pages: 196
ISBN-13: 9780521337038
DOWNLOAD EBOOKCombinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
Probability Theory of Classical Euclidean Optimization Problems
Author: Joseph E. Yukich
Publisher: Springer
Published: 2006-11-14
Total Pages: 162
ISBN-13: 354069627X
DOWNLOAD EBOOKThis monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists.
Geometry of Cuts and Metrics
Author: Michel Marie Deza
Publisher: Springer
Published: 2009-11-12
Total Pages: 580
ISBN-13: 3642042953
DOWNLOAD EBOOKCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
