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arXiv · 1605.04297

Growth rates of permutation classes: from countable to uncountable

Vincent Vatter
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Abstract

We establish that there is an algebraic number $ξ\approx 2.30522$ 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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Vincent Vatter. 2019-04-11. Growth rates of permutation classes: from countable to uncountable. https://arxiv.org/abs/1605.04297

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