Large infinite antichains of permutations
Michael H. Albert, Robert Brignall, and Vincent Vatter

TL;DR
This paper constructs infinite antichains of permutations with large growth rates, showing every proper permutation class is contained in one with a rational generating function, leveraging the Marcus-Tardos theorem.
Contribution
It introduces a method to construct infinite antichains with arbitrarily large growth rates and demonstrates their application to permutation class containment.
Findings
Existence of infinite antichains with arbitrarily large growth rates
Every proper permutation class is contained in a class with a rational generating function
Utilizes the Marcus-Tardos theorem in the proof
Abstract
Infinite antichains of permutations have long been used to construct interesting permutation classes and counterexamples. We prove the existence and detail the construction of infinite antichains with arbitrarily large growth rates. As a consequence, we show that every proper permutation class is contained in a class with a rational generating function. While this result implies the conclusion of the Marcus-Tardos theorem, that theorem is used in our proof.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Advanced Mathematical Identities
