Growth rates of permutation classes: from countable to uncountable

Vincent Vatter

Growth rates of permutation classes: from countable to uncountable

Combinatorics 2019-04-15 v3

Authors: Vincent Vatter

Abstract

We establish that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi,$ there are only countably many less than $\xi$ . 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 $\xi$ is completed in a subsequent paper.

Keywords

permutation classes growth rates generalized grid classes concentration countable sets uncountable sets algebraic number

Cite

@article{arxiv.1605.04297,
  title  = {Growth rates of permutation classes: from countable to uncountable},
  author = {Vincent Vatter},
  journal= {arXiv preprint arXiv:1605.04297},
  year   = {2019}
}

Comments

To appear in Proc. Lond. Math. Soc. (3)

Growth rates of permutation classes: from countable to uncountable

Abstract

Keywords

Cite

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