Correlation inequalities for linear extensions

TL;DR

This paper introduces new correlation inequalities for linear extensions of finite posets using combinatorial atlas technology, with applications to Young tableaux and Euler numbers.

Contribution

It presents novel correlation inequalities for linear extensions, including approximate independence results, and applies these to combinatorial objects like Young tableaux and Euler numbers.

Findings

Probabilities of random linear extensions are approximately independent.

New inequalities relate to Stanley's inequality.

Applications include bounds on Young tableaux and Euler numbers.

Abstract

We employ the combinatorial atlas technology to prove new correlation inequalities for the number of linear extensions of finite posets. These include the approximate independence of probabilities and expectations of values of random linear extensions, closely related to Stanley's inequality. We also give applications to the numbers of standard Young tableaux and to Euler numbers.