Permutation classes of every growth rate above 2.48188

TL;DR

This paper proves that permutation classes exist for every growth rate above approximately 2.48188, confirming a conjecture and expanding understanding of permutation class growth rates.

Contribution

It establishes the existence of permutation classes for all growth rates above a specific constant, solving a conjecture by Albert and Linton.

Findings

Permutation classes exist for all growth rates above 2.48188.

The critical growth rate is the root of a specific polynomial.

The result confirms a long-standing conjecture in permutation class theory.

Abstract

We prove that there are permutation classes (hereditary properties of permutations) of every growth rate (Stanley-Wilf limit) at least \lambda \approx 2.48187, the unique real root of x^5-2x^4-2x^2-2x-1, thereby establishing a conjecture of Albert and Linton.