Open AccessBook
A course in combinatorics
J.H. van Lint,Richard M. Wilson +1 more
TLDR
The second edition of a popular book on combinatorics as discussed by the authors is a comprehensive guide to the whole of the subject, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes.Abstract:
This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.read more
Citations
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Journal ArticleDOI
Expander graphs and their applications
S Hoory,Nathan Linial +1 more
TL;DR: Expander graphs were first defined by Bassalygo and Pinsker in the early 1970s, and their existence was proved in the late 1970s as discussed by the authors and early 1980s.
Journal ArticleDOI
The geometry of graphs and some of its algorithmic applications
TL;DR: Efficient algorithms for embedding graphs low-dimensionally with a small distortion, and a new deterministic polynomial-time algorithm that finds a (nearly tight) cut meeting this bound.
MonographDOI
Random Graphs and Complex Networks
TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.
Journal ArticleDOI
Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists
TL;DR: A wide-ranging survey of general kernels of the Marcus-Lushnikov model of stochastic coalescence and the underlying deterministic approximation given by the Smoluchowski coagulation equations is attempted.
Journal ArticleDOI
Visual Cryptography for General Access Structures
TL;DR: This paper examines graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme, and provides a novel technique for realizing threshold visual cryptography schemes.
References
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Journal ArticleDOI
On a Problem of Formal Logic
TL;DR: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula.
Journal ArticleDOI
On the Shannon capacity of a graph
TL;DR: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.
Book
Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
Journal ArticleDOI
Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),
Journal ArticleDOI
A class of multiple-error-correcting codes and the decoding scheme
TL;DR: A class of multiple-error-correcting codes and their decoding scheme to device a coding scheme which is able to detect and correct such errors.