turkmath.org

Fence posets are combinatorial objects that come up in a  variety of settings, including cluster algebras, quiver representations, snake graphs and continued fractions. We will show that the rank polynomials corresponding to these posets are unimodal, proving a conjecture by Ovsienko and Morier-Genoud. We will introduce the more generalized framework of oriented posets where rank polynomials are replaced with rank matrices, and show applications in cluster algebras and polytopes. Partially based on joint work with Cem Yalım Özel, Mohan Ravichandran and Emine Yıldırım.