BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sam Hopkins (Howard University) DTSTART:20241012T150000Z DTEND:20241012T160000Z DTSTAMP:20260419T114607Z UID:MAAGC2024/4 DESCRIPTION:Title: Upho posets\nby Sam Hopkins (Howard University) as part of MAAGC 202 4\n\n\nAbstract\nA partially ordered set is called upper homogeneous\, or “upho\,” if every principal order filter is isomorphic to the whole po set. This class of fractal-like posets was recently introduced by Stanley. Our first observation is that the rank generating function of a (finite t ype N-graded) upho poset is the reciprocal of its characteristic generatin g function. This means that each upho lattice has associated to it a finit e graded lattice\, called its core\, that determines its rank generating f unction. With an eye towards classifying upho lattices\, we investigate wh ich finite graded lattices arise as cores\, providing both positive and ne gative results. Our overall goal for this talk is to advertise upho posets \, and especially upho lattices\, which we believe are a natural and rich class of posets deserving of further attention. Essentially no background knowledge will be assumed\, and we also hope to highlight several open pro blems.\n LOCATION:https://researchseminars.org/talk/MAAGC2024/4/ END:VEVENT END:VCALENDAR