Preprint Article Version 1 This version is not peer-reviewed

What do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know About Each Other?

Version 1 : Received: 21 August 2019 / Approved: 23 August 2019 / Online: 23 August 2019 (11:35:32 CEST)

How to cite: Itskovich, E.J.; Levit, V.E. What do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know About Each Other?. Preprints 2019, 2019080247 (doi: 10.20944/preprints201908.0247.v1). Itskovich, E.J.; Levit, V.E. What do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know About Each Other?. Preprints 2019, 2019080247 (doi: 10.20944/preprints201908.0247.v1).

Abstract

As a kind of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.

Subject Areas

Erd˝os-Szekeres theorem; longest increasing sequence; longest decreasing sequence

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