Intervals of permutation class growth rates
Bevan, David (2018) Intervals of permutation class growth rates. Combinatorica, 38 (2). pp. 279-303. ISSN 1439-6912
|
Text (Bevan-Combinatorica-2016-Intervals-of-permutations-class-growth)
Bevan_Combinatorica_2016_Intervals_of_permutations_class_growth.pdf Accepted Author Manuscript Download (388kB)| Preview |
Abstract
We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θB ≈ 2.35526, and that it also contains every value at least λB ≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λA ≈ 2.48187. Thus, we also refute his conjecture that the set of growth rates below λA is nowhere dense. Our proof is based upon an analysis of expansions of real numbers in non-integer bases, the study of which was initiated by Rényi in the 1950s. In particular, we prove two generalisations of a result of Pedicini concerning expansions in which the digits are drawn from sets of allowed values.
Creators(s): |
Bevan, David ![]() | Item type: | Article |
---|---|
ID code: | 57976 |
Keywords: | permutation classes, growth rates, expansions in noninteger bases, Mathematics, Discrete Mathematics and Combinatorics |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Computer and Information Sciences |
Depositing user: | Pure Administrator |
Date deposited: | 28 Sep 2016 14:54 |
Last modified: | 17 Jan 2021 03:00 |
URI: | https://strathprints.strath.ac.uk/id/eprint/57976 |
Export data: |