What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?

What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?

As a kind of converse of the celebrated Erdős&#8722;Szekeres theorem, we present a necessary and sufficient condition for a sequence of length <i>n</i> to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths <i>x</i> and <i>...

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Bibliographic Details
Main Authors: Elizabeth J. Itskovich, Vadim E. Levit
Format: Article
Language:English
Published: MDPI AG 2019-11-01
Series:Algorithms
Subjects:
erdős–szekeres theorem
longest increasing sequence
longest decreasing sequence
Online Access:https://www.mdpi.com/1999-4893/12/11/237
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spelling doaj-5d5af4d697254270a9a2a3af637985be2020-11-24T21:55:32ZengMDPI AGAlgorithms1999-48932019-11-01121123710.3390/a12110237a12110237What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?Elizabeth J. Itskovich0Vadim E. Levit1Department of Computer Science, Ariel University, Ariel 40700, IsraelDepartment of Computer Science, Ariel University, Ariel 40700, IsraelAs a kind of converse of the celebrated Erdős&#8722;Szekeres theorem, we present a necessary and sufficient condition for a sequence of length <i>n</i> to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths <i>x</i> and <i>y</i>, respectively.https://www.mdpi.com/1999-4893/12/11/237erdős–szekeres theoremlongest increasing sequencelongest decreasing sequence
collection DOAJ
language English
format Article
sources DOAJ
author Elizabeth J. Itskovich
Vadim E. Levit
spellingShingle Elizabeth J. Itskovich
Vadim E. Levit
What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
Algorithms
erdős–szekeres theorem
longest increasing sequence
longest decreasing sequence
author_facet Elizabeth J. Itskovich
Vadim E. Levit
author_sort Elizabeth J. Itskovich
title What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
title_short What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
title_full What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
title_fullStr What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
title_full_unstemmed What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
title_sort what do a longest increasing subsequence and a longest decreasing subsequence know about each other?
publisher MDPI AG
series Algorithms
issn 1999-4893
publishDate 2019-11-01
description As a kind of converse of the celebrated Erdős&#8722;Szekeres theorem, we present a necessary and sufficient condition for a sequence of length <i>n</i> to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths <i>x</i> and <i>y</i>, respectively.
topic erdős–szekeres theorem
longest increasing sequence
longest decreasing sequence
url https://www.mdpi.com/1999-4893/12/11/237
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