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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 &gt; 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

  • Czech description

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