Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10123634" target="_blank" >RIV/00216208:11320/12:10123634 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jcta.2012.05.006" target="_blank" >http://dx.doi.org/10.1016/j.jcta.2012.05.006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcta.2012.05.006" target="_blank" >10.1016/j.jcta.2012.05.006</a>

Result language
angličtina
Original language name
Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns
Original language description
We prove that the Stanley-Wilf limit of any layered permutation pattern of length L is at most 4L^2, and that the Stanley-Wilf limit of the pattern 1324 is at most 16. These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. We also conjecture that, for any k, the set of 1324-avoiding permutations with k inversions contains at least as many permutations of length n + 1 as those of length n. We show that if this is true then the Stanley-Wilf limit for 1324 is at most e^(pi sqrt{2/3}).
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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