This book describes conjectures and unsolved problems in Ramsey theory
and proposes new ones, focusing on the relations between different problems, rather than choosing problems that are believed to be more important, famous, or difficult.
Keywords: Geometric Ramsey theory
, Erdos-Hajnal property, incidence bounds
This definition was subsequently developed into Ramsey theory
by Graham, Rothschild and Spencer .
He developed a proof in a field of mathematics known as Ramsey theory
. It focuses on finding patterns in large and complicated systems.
The topics are basic counting methods, generating functions, the pigeonhole principle, Ramsey theory
, error-correcting codes, and combinatorial designs.
Roughly speaking Ramsey theory
states that complete disorder is impossible .
Along with the exercises come both hints and solutions as he works through basic enumeration, the sieve process, permutations, classical enumeration problems in graph theory, parity and duality, connectivity, factors of graphs, independent sets of points, chromatic number, problems for graphs, the spectra of graphs and random walks, automorphisms of graphs, hypergraphs, Ramsey theory
He claims that "regulators have accepted the usefulness of Ramsey theory
," a claim which is open to lively debate.
An Introduction to Ramsey Theory
: Fast Functions, Infinity, and Metamathematics
Mathematics of Ramsey Theory
, Springer, Berlin, Alorithms and Combin.
Second place, and a $75,000 scholarship, went to Jacob Licht, 17, of West Hartford, Conn., for his mathematical research into Rainbow Ramsey theory
, which states that patterns must exist even within disorder.
The party puzzle typifies the sorts of problems that Ramsey theory
tackles: What is the minimum number of guests that must be invited so that either at least x guests will know one another or at least y guests won't?