Correlation inequalities for linear extensions

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.

25 pages, 1 figure. Added counterexample to Conjecture 3.8 in v1. To appear in Advances in Mathematics

References in corpus (13)

• Hook formulas for skew shapes I. $q$-analogues and bijections
• Mixed volumes and the Bochner method
• Correlation bounds for fields and matroids
• A combinatorial model for computing volumes of flow polytopes
• Introduction to the combinatorial atlas
• Extensions of the Kahn--Saks inequality for posets of width two
• The cross-product conjecture for width two posets
• Equality cases of the Alexandrov--Fenchel inequality are not in the polynomial hierarchy
• Effective poset inequalities
• The mystery of plethysm coefficients
• A positivity conjecture on the structure constants of shifted Jack functions
• Multivariate correlation inequalities for $P$-partitions
• On the cross-product conjecture for the number of linear extensions