Density maximizers of layered permutations

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dc.contributor.authorKabela, Adam
dc.contributor.authorKráľ, Daniel
dc.contributor.authorNoel, Jonathan A.
dc.contributor.authorPierron, Théo
dc.date.accessioned2023-02-20T11:00:25Z
dc.date.available2023-02-20T11:00:25Z
dc.date.issued2022
dc.description.abstract-translatedA 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.en
dc.format23 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationKABELA, A. KRÁĽ, D. NOEL, JA. PIERRON, T. Density maximizers of layered permutations. ELECTRONIC JOURNAL OF COMBINATORICS, 2022, roč. 29, č. 3, s. nestránkováno. ISSN: 1077-8926cs
dc.identifier.document-number913376700001
dc.identifier.doi10.37236/10781
dc.identifier.issn1077-8926
dc.identifier.obd43937287
dc.identifier.uri2-s2.0-85137349290
dc.identifier.urihttp://hdl.handle.net/11025/51528
dc.language.isoenen
dc.project.IDGA20-09525S/Strukturální vlastnosti tříd grafů charakterizovaných zakázanými indukovanými podgrafycs
dc.publisherAustralian National Universityen
dc.relation.ispartofseriesElectronic Journal Of Combinatoricsen
dc.rights© authorsen
dc.rights.accessopenAccessen
dc.subject.translatedpermutation densityen
dc.subject.translatedlayered permutationen
dc.titleDensity maximizers of layered permutationsen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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