Independence of permutation limits at infinitely many scales

TL;DR

This paper introduces a new way to analyze permutation limits across multiple scales, demonstrating that these limits can be independently chosen at infinitely many scales, which advances understanding of permutation structure.

Contribution

It presents a novel notion of convergence for permutations at various scales and proves the independence of limits at infinitely many scales, a significant theoretical development.

Findings

Limits can be chosen independently at infinitely many scales.

A new notion of convergence based on pattern density at restricted widths.

Establishment of independence of permutation limits across multiple scales.

Abstract

We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite number of scales.