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On Free Semigroups and Ramsey Numbers
Published online by Cambridge University Press: 20 November 2018
Abstract
If the length of a word w in a free semigroup F(X) satisfies , then for every partition of F(X) into k classes, w has n consecutive factors of length ≥p in the same class. As a consequence, the diagonal Ramsey numbers R(pn+1, p+1, k) have 1+pnk as lower bound.
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- Copyright © Canadian Mathematical Society 1974