BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Laura Colmenarejo (UMass Amherst)
DTSTART:20210412T190000Z
DTEND:20210412T200000Z
DTSTAMP:20260423T005708Z
UID:YUAAS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YUAAS/29/">C
 hromatic symmetric functions for Dyck paths and $q$-rook theory</a>\nby La
 ura Colmenarejo (UMass Amherst) as part of York University Applied Algebra
  Seminar\n\n\nAbstract\n"Given a graph and a set of colors\, a coloring is
  a function that associates each vertex in the graph with a color. In 1995
 \, Stanley generalized this definition to symmetric functions by looking a
 t the number of times each color is used and extending the set of colors t
 o $\\mathbb{Z}^+$. In 2012\, Shareshian and Wachs introduced a refinement 
 of the chromatic functions for ordered graphs as $q$-analogues.\n\nIn the 
 particular case of Dyck paths\, Stanley and Stembridge described the conne
 ction between chromatic symmetric functions of abelian Dyck paths and squa
 re hit numbers\, and Guay-Paquet described their relation to rectangular h
 it numbers. Recently\, Abreu-Nigro generalized the former connection for t
 he Shareshian-Wachs $q$-analogue\, and in unpublished work\, Guay-Paquet g
 eneralized the latter.  \n\nIn this talk\, I want to give an overview of t
 he framework and present another proof of Guay-Paquet's identity using $q$
 -rook theory. Along the way\, we will also discuss $q$-hit numbers\, two v
 ariants of their statistic\, and some deletion-contraction relations. This
  is recent work with Alejandro H. Morales and Greta Panova. "\n
LOCATION:https://researchseminars.org/talk/YUAAS/29/
END:VEVENT
END:VCALENDAR