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UID:20261015T141103EDT-5096uhuRPp@132.216.98.100
DTSTAMP:20261015T181103Z
DESCRIPTION:Title: The primitive Eulerian polynomial.\n\nAbstract: We intro
 duce the Primitive Eulerian polynomial $P_mathcal{A}(z)$ of a central hype
 rplane Arrangement $mathcal{A}$. It is a reparametrization of the cocharac
 teristic polynomial of the arrangement. Previous work (2021) implicitly sh
 owed that this polynomial has nonnegative coefficients in the simplicial c
 ase. If $mathcal{A}$ 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)excedance statistic on a particular subset of $W$. No interpreta
 tion was found for reflection arrangements of type D.\n	\n	We present an alt
 ernative geometric and combinatorial interpretation for the coefficients o
 f $P_mathcal{A}(z)$ for all simplicial arrangements $mathcal{A}$. For refl
 ection arrangements of types A\, B\, and D\, we find recursive formulas th
 at mirror those for the Eulerian polynomial of the corresponding type. We 
 also present real-rootedness results and conjectures for $P_mathcal{A}(z)$
 . This is joint work with Christophe Hohlweg and Franco Saliola.\n\nPK-432
 3\, UQAM\, 201\, av du Président-Kennedy\n\nWeb site : https://lacim.uqam.
 ca/seminaires/\n
DTSTART:20221007T150000Z
DTEND:20221007T160000Z
SUMMARY:Jose Bastidas\, LACIM
URL:https://www.mcgill.ca/mathstat/channels/event/jose-bastidas-lacim-34242
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