Ramsey theory


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Ramsey theory

[′ram·zē ‚thē·ə·rē]
(mathematics)
The theory of order that must exist in subsets of sufficiently large sets, as illustrated by Ramsey's theorem and van der Waerden's theorem.
References in periodicals archive ?
Keywords: Geometric Ramsey theory, Erdos-Hajnal property, incidence bounds
He developed a proof in a field of mathematics known as Ramsey theory.
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 and reconstruction.
He claims that "regulators have accepted the usefulness of Ramsey theory," a claim which is open to lively debate.
Licht has made several original contributions in a new multicolor variant, Rainbow Ramsey theory.
Olaf College in June 1979 on the basic foundations of Ramsey theory.
Mathematics of Ramsey Theory, Springer, Berlin, Alorithms and Combin.
for his mathematical research into Rainbow Ramsey theory, which states that patterns must exist even within disorder.
Exploring a variety of topics from the field of Ramsey theory within the set of integers, Landman and Robertson introduce students to mathematical research, giving them an appreciation for the essence of mathematical research and getting them started on their own research work among the unsolved problems in the flourishing area of Ramsey theory on the integers.
This result stems from a branch of pure mathematics known as Ramsey theory, which concerns the existence of highly regular patterns in any large set of randomly selected numbers, points, or objects.