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DESCRIPTION: Many polynomials arising in combinatorics are known or conject
 ured to have only real roots. One approach to these questions is to study t
 ransformations that preserve the real-rootedness property. This talk is cen
 tered around the Eulerian transformation which is the linear transformation
  that sends the i-th standard monomial to the i-th Eulerian polynomial. Eul
 erian polynomials appear in various guises in enumerative and geometric com
 binatorics and have many favorable properties\, in particular\, they are re
 al-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 o
 n binomial Eulerian polynomials and provide enumerative and geometric inter
 pretations. This is joint work with Petter Brändén. 
DTSTAMP:20220503T000200
DTSTART:20220523T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)\n 
SEQUENCE:0
SUMMARY:Katharina Jochemko (KTH Stockholm): The Eulerian transformation
UID:107920348@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20220523-L-Joc
 hemko.html
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