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SUMMARY:Jose Bastidas (LACIM)
DTSTART;VALUE=DATE-TIME:20221007T150000Z
DTEND;VALUE=DATE-TIME:20221007T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T062626Z
UID:Combinatorics/47
DESCRIPTION:Title: The primitive Eulerian polynomial\nby Jose Bastidas (LACIM) as
part of CRM-SÃ©minaire du LACIM\n\n\nAbstract\nWe introduce the Primitive
Eulerian polynomial $P_\\mathcal{A}(z)$ of a central hyperplane Arrangemen
t $\\mathcal{A}$. It is a reparametrization of the cocharacteristic polyno
mial of the arrangement. Previous work (2021) implicitly showed that this
polynomial has nonnegative coefficients in the simplicial case. If $\\math
cal{A}$ is the arrangement corresponding to a Coxeter group $W$ of type A
or B\, then $P_\\mathcal{A}(z)$ is the generating function for the (flag)e
xcedance statistic on a particular subset of $W$. No interpretation was fo
und for reflection arrangements of type D. \n \nWe present an alternative
geometric and combinatorial interpretation for the coefficients of $P_\\ma
thcal{A}(z)$ for all simplicial arrangements $\\mathcal{A}$. For reflectio
n arrangements of types A\, B\, and D\, we find recursive formulas that mi
rror those for the Eulerian polynomial of the corresponding type. We also
present real-rootedness results and conjectures for $P_\\mathcal{A}(z)$. T
his is joint work with Christophe Hohlweg and Franco Saliola.\n
LOCATION:https://researchseminars.org/talk/Combinatorics/47/
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