Growth Rates of Permutation Classes: Categorization Up to the Uncountability Threshold
Israel Journal of Mathematics
Original Item ID
In the antecedent paper to this it was established 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. Here we provide a complete characterization of the growth rates less than ξ. In particular, this classification establishes that ξ is the least accumulation point from above of growth rates and that all growth rates less than or equal to ξ are achieved by finitely based classes. A significant part of this classification is achieved via a reconstruction result for sum indecomposable permutations. We conclude by refuting a suggestion of Klazar, showing that ξ is an accumulation point from above of growth rates of finitely based permutation classes.
Pantone, Jay and Vatter, Vincent, "Growth Rates of Permutation Classes: Categorization Up to the Uncountability Threshold" (2020). Mathematical and Statistical Science Faculty Research and Publications. 127.