Preprints.org logo
Preprint
Article

This version is not peer-reviewed.

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

A peer-reviewed article of this preprint also exists.

Submitted:

21 August 2019

Posted:

23 August 2019

You are already at the latest version

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.
Keywords: 
Erd˝os-Szekeres theorem
;  
longest increasing sequence
;  
longest decreasing sequence
Subject: 
Computer Science and Mathematics  -   Computational Mathematics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.