Growth rates of permutation classes: from countable to uncountable | Zendy

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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

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.

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