Date:

Location:

CB 307

Speaker(s) / Presenter(s):

Ford McElroy, University of Kentucky

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.

Type of Event (for grouping events):