Title:	Density maximizers of layered permutations
Authors:	Kabela, Adam Kráľ, Daniel Noel, Jonathan A. Pierron, Théo
Citation:	KABELA, A. KRÁĽ, D. NOEL, JA. PIERRON, T. Density maximizers of layered permutations. ELECTRONIC JOURNAL OF COMBINATORICS, 2022, roč. 29, č. 3, s. nestránkováno. ISSN: 1077-8926
Issue Date:	2022
Publisher:	Australian National University
Document type:	článek article
URI:	2-s2.0-85137349290 http://hdl.handle.net/11025/51528
ISSN:	1077-8926
Keywords in different language:	permutation density;layered permutation
Abstract in different language:	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.
Rights:	© authors
Appears in Collections:	Články / Articles (KMA) OBD

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