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Lecture by Katharina Jochemko (KTH Stockholm): The Eulerian transformation

May 23, 2022 | 02:15 PM

Many polynomials arising in combinatorics are known or conjectured to have only real roots. One approach to these questions is to study transformations that preserve the real-rootedness property. This talk is centered around the Eulerian transformation which is the linear transformation that sends the i-th standard monomial to the i-th Eulerian polynomial. Eulerian polynomials appear in various guises in enumerative and geometric combinatorics and have many favorable properties, in particular, they are real-rooted and symmetric. We discuss how these properties carry over to the Eulerian transformation. In particular, we disprove a conjecture by Brenti (1989) concerning the preservation of real roots, extend recent results on binomial Eulerian polynomials and provide enumerative and geometric interpretations. This is joint work with Petter Brändén.

Time & Location

May 23, 2022 | 02:15 PM

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
Room 005 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)