Average length of the longest $k$ -alternating subsequence

preprint2015arXivOpen access

We prove a conjecture of Drew Armstrong on the average maximal length of $k$ -alternating subsequence of permutations. The $k=1$ case is a well-known result of Richard Stanley.

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Average length of the longest $k$ -alternating subsequence

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Average length of the longest kkk-alternating subsequence

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Average length of the longest $k$ -alternating subsequence