Poset inequalities

The lectures will give an overview of poset inequalities with emphasis on counting the number of linear extensions. I will follow our recent survey, hoping to include or at least sketch as many proofs as possible, time permitting.

• Lecture 1: Linear extensions and order polynomials, basic inequalities, several direct combinatorial proofs of the Bjorner-Wachs inequality.
• Lecture 2: Chain and order polytopes, their volume and Ehrhart polynomials, Sidorenko inequality.
• Lecture 3: FKG inequality, intransitivity phenomenon, applications to XYZ, Fishburn and Lam-Pylyavskyy inequalities.
• Lecture 4: Stanley inequality, Part I. Proofs via geometry and combinatorial atlas.
• Lecture 5: Stanley inequality, Part II. Equality conditions and complexity aspects.