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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
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SUMMARY:Katharina Jochemko (KTH Stockholm): The Eulerian transformation
UID:107920348@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220523-L-Jochemko.html
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