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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)
A peer-reviewed article of this Preprint also exists.
Itskovich, E.J.; Levit, V.E. What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other? Algorithms 2019, 12, 237. Itskovich, E.J.; Levit, V.E. What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other? Algorithms 2019, 12, 237.
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 is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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