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Prove that (4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13) is a sequence of length 42with no monotone subsequence of length 5. Generalize this example to find, for everyn, a sequence of

  1. Prove that (4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13) is a sequence of length 42with no monotone subsequence of length 5. Generalize this example to find, for everyn, a sequence of lengthn2with no monotone subsequence of lengthn+ 1.

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