Small permutation classes release_ohni3j7emngnzautbn3wlrjumi

by Vincent Vatter

Released as a paper-conference .

2016  

Abstract

We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number κ, approximately 2.20557, for which there are only countably many permutation classes of growth rate (Stanley-Wilf limit) less than κ but uncountably many permutation classes of growth rate κ, answering a question of Klazar. We go on to completely characterize the possible sub-κ growth rates of permutation classes, answering a question of Kaiser and Klazar. Central to our proofs are the concepts of generalized grid classes (introduced herein), partial well-order, and atomicity (also known as the joint embedding property).
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Type  paper-conference
Stage   accepted
Date   2016-04-05
Version   v3
Language   en ?
arXiv  0712.4006v3
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