Densities in large permutations and parameter testing

TL;DR

This paper extends a classical graph theory result to permutations, demonstrating independence of substructure densities, and introduces a permutation parameter that is finitely approximable but not finitely forcible, answering an open question.

Contribution

It proves an analogue of a graph theorem for permutations and provides a counterexample to finite forcibility in permutation parameters.

Findings

Densities of connected subpermutations are independent in large permutations.

Existence of a finitely approximable but not finitely forcible permutation parameter.

Addresses an open question in permutation parameter theory.

Abstract

A classical theorem of Erdos, Lovasz and Spencer asserts that the densities of connected subgraphs in large graphs are independent. We prove an analogue of this theorem for permutations and we then apply the methods used in the proof to give an example of a finitely approximable permutation parameter that is not finitely forcible. The latter answers a question posed by two of the authors and Moreira and Sampaio.