Growth rates of permutation classes: from countable to uncountable

2016/05/13 by Vatter, Vincent
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04297

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.

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