Titlebook: Ramsey Theory for Discrete Structures; Hans Jürgen Prömel Book 2013 Springer International Publishing Switzerland 2013 Ramsey theory.combi

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Hans Jürgen Prömel moved on from a prehistoric interest in metals, chert andclay, to become a modern science, utilizing sophisticated techniquesto understand the Earth‘s processes and evolution. By looking deeplyinto the Earth‘s constituents, scientists are able to verify theorieson its formation and, by corollary, o

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From Hilbert’s Cube Lemma to Rado’s ThesisQuite a while before Ramsey proved his partition theorem for finite sets some results have been established which can be viewed as the earliest roots of Ramsey theory. The probably first one is due to David Hilbert (1892).

Enthralling

Hales-Jewett’s TheoremTic-Tac-Toe is a game played by two people writing the symbols O and X in turn on a pattern of nine squares with the purpose of getting three such marks in a row. Of course, the traditional 3 × 3 Tic-Tac-Toe need not to have a winner, the second player can achieve a tie.

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Ramsey NumbersThe finite version of Ramsey’s theorem asserts that for every triple ., . and . of positive integers there exists a positive integer . such that . → (.). .. In Sect. . a compactness argument was used to derive this result from the infinite Ramsey theorem not giving any information about the size of .

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