BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Bruce Sagan (Michigan State University)
DTSTART:20201124T160000Z
DTEND:20201124T170000Z
DTSTAMP:20260423T021142Z
UID:OCAS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OCAS/14/">On
  a rank-unimodality conjecture of Morier-Genoud and Ovsienko</a>\nby Bruce
  Sagan (Michigan State University) as part of Online Cluster Algebra Semin
 ar (OCAS)\n\n\nAbstract\nLet $\\alpha=(a\,b\,\\ldots)$ be a composition\, 
 that is\, a finite sequence of positive integers.  Consider the associated
  partially ordered set $F(\\alpha)$\, called a fence\, whose covering rela
 tions are\n$$                                                             
                                                                           
                                                                     \nx_1\
 \lhd x_2 \\lhd \\ldots\\lhd x_{a+1}\\rhd x_{a+2}\\rhd \\ldots\\rhd x_{a+b+
 1}\\lhd x_{a+b+2}\\lhd \\ldots\\ .                                        
                                                                  \n$$\nWe 
 study the associated distributive lattice $L(\\alpha)$ consisting of all l
 ower order ideals of $F(\\alpha)$.\nThese lattices are important in the th
 eory of cluster algebras and their rank generating functions can be used t
 o define $q$-analogues of rational numbers.\nWe make progress on a recent 
 conjecture of Morier-Genoud and Ovsienko that $L(\\alpha)$ is rank unimoda
 l.\nAll terms from the theory of partially ordered sets will be carefully 
 defined.  This is joint work with Thomas McConville and Clifford Smyth.\n
LOCATION:https://researchseminars.org/talk/OCAS/14/
END:VEVENT
END:VCALENDAR