Correlation inequalities for linear extensions
Combinatorics
2024-12-02 v2 Probability
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.
Cite
@article{arxiv.2211.16637,
title = {Correlation inequalities for linear extensions},
author = {Swee Hong Chan and Igor Pak},
journal= {arXiv preprint arXiv:2211.16637},
year = {2024}
}
Comments
25 pages, 1 figure. Added counterexample to Conjecture 3.8 in v1. To appear in Advances in Mathematics