The limit of a Stanley-Wilf sequence is not always rational, and layered patterns beat monotone patterns

dc.creatorBona, Miklos
dc.date2004-03-29
dc.date2004-05-13
dc.date.accessioned2026-07-07T05:06:52Z
dc.date.available2026-07-07T05:06:52Z
dc.descriptionWe show the first known example for a pattern $q$ for which $\lim_{n\to \infty} \sqrt[n]{S_n(q)}$ is not an integer. We find the exact value of the limit and show that it is irrational. Then we generalize our results to an infinite sequence of patterns. Finally, we provide further generalizations that start explaining why certain patterns are easier to avoid than others. Finally, we show that if $q$ is a layered pattern of length $k$, then $L(q)\geq (k-1)^2$ holds.
dc.description10 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0403502
dc.identifierhttp://arxiv.org/abs/math/0403502
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70637
dc.subjectCombinatorics
dc.subject05A05
dc.titleThe limit of a Stanley-Wilf sequence is not always rational, and layered patterns beat monotone patterns
dc.typetext

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