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Growth rates of permutation classes: from countable to uncountable
Author(s) -
Vatter Vincent
Publication year - 2019
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12250
Subject(s) - uncountable set , countable set , mathematics , permutation (music) , algebraic number , property (philosophy) , cyclic permutation , combinatorics , discrete mathematics , symmetric group , mathematical analysis , philosophy , physics , epistemology , acoustics
Abstract We establish that there is an algebraic number ξ ≈ 2.30522 such that while there are uncountably many growth rates of permutation classes arbitrarily close to ξ , there are only countably many less than ξ . Central to the proof are various structural notions regarding generalized grid classes and a new property of permutation classes called concentration. The classification of growth rates up to ξ is completed in a subsequent paper.