Masters Exam

Speaker:  Ford McElroy, University of Kentucky

Title:         The Eulerian Transformation and Real-Rootedness

Abstract:

Many combinatorial polynomials are known to be real-rooted. Many others are conjectured to be real-rooted. The Eulerian Transformation is a map from A:R[t] --> R[t] generated by A(t^n)= A_n(t), the nth Eulerian polynomial. Brenti (1989) conjectured that the Eulerian Transformation preserves real-rootedness. In the 2022 paper The Eulerian Transformation by Brändén and Jochemko, they disprove Brenti's conjecture and make one of their own. In the talk, we will look at

 (i) polynomial properties related to real-rootedness, 

(ii) Brändén and Jochemko's counterexample to Brenti's conjecture

(iii) evidence Brändén and Jochemko provide to support their conjecture.