Density maximizers of layered permutations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43966287" target="_blank" >RIV/49777513:23520/22:43966287 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14330/22:00127928
Result on the web
<a href="https://doi.org/10.37236/10781" target="_blank" >https://doi.org/10.37236/10781</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/10781" target="_blank" >10.37236/10781</a>
Alternative languages
Result language
angličtina
Original language name
Density maximizers of layered permutations
Original language description
A permutation is layered if it contains neither 231 nor 312 as a pattern. It is known that, if σ is a layered permutation, then the density of σ in a permutation of order n is maximized by a layered permutation. Albert, Atkinson, Handley, Holtonand Stromquist [Electron. J. Combin. 9 (2002), #R5] claimed that the density of a layered permutation with layers of sizes (a,1,b) where a,b > 2 is asymptotically maximized by layered permutations with a bounded number of layers, and conjectured that the same holds if a layered permutation has no consecutive layers of size one and its first and last layers are of size at least two. We show that, if σ is a layered permutation whose first layer is sufficiently large and second layer is of size one, then the number of layers tends to infinity in every sequence of layered permutations asymptotically maximizing the density of σ. This disproves the conjecture and the claim of Albert et al. We complement this result by giving sufficient conditions on a layered permutation to have asymptotic or exact maximizers with a bounded number of layers.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-09525S" target="_blank" >GA20-09525S: Structural properties of graph classes characterized by forbidden subgraphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ELECTRONIC JOURNAL OF COMBINATORICS
ISSN
1077-8926
e-ISSN
1077-8926
Volume of the periodical
29
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
nestrankovano
UT code for WoS article
000913376700001
EID of the result in the Scopus database
2-s2.0-85137349290