A Note on a Ramsey-Type Problem for Sequences

Abstract

Two sequences {xi}i=1 and {yi}i=1 of distinct integers are similar if their entries are order-isomorphic. Let f(r,X) be the length of the shortest sequence Y such that any r-coloring of the entries of Y yields a monochromatic subsequence that is also similar to X. In this note we show that for any fixed non-monotone sequence X, f(r,X) = Θ(r2), otherwise… (More)

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