About: On growth rates of closed permutation classes

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A class of permutations $\Pi$ is called closed if $\pi\subset\sigma\in\Pi$ implies $\pi\in\Pi$, where the relation $\subset$ is the natural containment of permutations. Let $\Pi_n$ be the set of all permutations of $1,2,\dots,n$ belonging to $\Pi$. W e investigate the counting functions $n\mapsto\|\Pi_n\|$ of closed classes. Our main result says that if $\|\Pi_n\|<2^{n-1}$ for at least one $n\ge 1$, then there is a unique $k\ge 1$ such that $F_{n,k}\le \|\Pi_n\|\le F_{n,k}\cdot n^c$ holds for all $n\ge 1$ with a constant $c>0$. Here $F_{n,k}$ are the generalized Fibonacci numbers which grow like powers of the largest positive root of $x^k-x^{k-1}-\cdots-1$. We characterize also the constant and the polynomial growth of closed permutation classes a nd give two more results on these. A class of permutations $\Pi$ is called closed if $\pi\subset\sigma\in\Pi$ implies $\pi\in\Pi$, where the relation $\subset$ is the natural containment of permutations. Let $\Pi_n$ be the set of all permutations of $1,2,\dots,n$ belonging to $\Pi$. W e investigate the counting functions $n\mapsto\|\Pi_n\|$ of closed classes. Our main result says that if $\|\Pi_n\|<2^{n-1}$ for at least one $n\ge 1$, then there is a unique $k\ge 1$ such that $F_{n,k}\le \|\Pi_n\|\le F_{n,k}\cdot n^c$ holds for all $n\ge 1$ with a constant $c>0$. Here $F_{n,k}$ are the generalized Fibonacci numbers which grow like powers of the largest positive root of $x^k-x^{k-1}-\cdots-1$. We characterize also the constant and the polynomial growth of closed permutation classes a nd give two more results on these. (en)
Title	On growth rates of closed permutation classes On growth rates of closed permutation classes (en)
skos:prefLabel	On growth rates of closed permutation classes On growth rates of closed permutation classes (en)
skos:notation	RIV/49777513:23520/03:00000145!RIV/2004/MSM/235204/N
http://linked.open.../vavai/riv/strany	1-20
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LN00A056), Z(MSM 113200005), Z(MSM 235200001)
http://linked.open...iv/cisloPeriodika	0
http://linked.open...vai/riv/dodaniDat	2004
http://linked.open...aciTvurceVysledku	Kaiser, Tomáš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	619367
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/03:00000145
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	permutation;closed class;permutation containment;Stanley-Wilf conjecture (en)
http://linked.open.../riv/klicoveSlovo	permutation Stanley-Wilf conjecture closed class permutation containment
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[360C8DF51922]
http://linked.open...i/riv/nazevZdroje	Electronic Journal of Combinatorics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute of Theoretical Computer Science (Center of Young Science)
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	Neuveden
http://linked.open...iv/tvurceVysledku	Kaiser, Tomáš Klazar, Martin
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20235200001 http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20113200005
issn	1097-1440
number of pages	20 (xsd:int)
http://localhost/t...ganizacniJednotka	23520

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