@MISC{Klazar94alinear, author = {Martin Klazar}, title = {A Linear Upper Bound in Extremal Theory of Sequences}, year = {1994} }

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Abstract

An extremal problem considering sequences related to Davenport-Schinzel sequences is investigated in this paper. We prove that f(x k ; n) = O(n) where the quantity on the left side is defined as the maximum length m of the sequence u = a 1 a 2 ::a m of integers such that 1) 1 a r n, 2) a r = a s ; r 6= s implies jr \Gamma sj k and 3) u contains no subsequence of the type x k (x stands for xx::x i-times).