Discrete Geometry and Combinatorics Seminar
For any finite partially ordered set P, the P-Eulerian polynomial is the generating function for descents over the set of linear extensions of P. Here we study the Zn-Eulerian polynomials, where Zn denotes a naturally labeled zig-zag poset on n elements. By a result of Brändén, these polynomials are gamma-nonnegative, and hence the coefficients are symmetric and unimodal. These polynomials have appeared directly or indirectly in about half a dozen distinct contexts (from magic labelings of graphs to the study of hydrocarbons), but have not been studied systematically. We will survey new and old results, and point to some open questions. This work is joint with Yan Zhuang.