Wednesday, November 13, 2019 at 4:15pm to 5:15pm
Room 2-139 -- MIT - Dept. of Mathematics, 77 Mass. Ave., Cambridge, MA
SPEAKER: Ricahrd Stanley (Massachusetts Institute of Technology)
TITLE: Upper homogeneous posets
A poset P is called upper homogeneous if for all t in P, the principal dual order ideal Vt = s in P : s >= t is isomorphic to P. We will be concerned with the case when P is graded and has finitely many elements of each rank. In that case a quasisymmetric generating function FP (due to Richard Ehrenborg) for the flag f-vector of P is a symmetric function. We will give some interesting examples and then discuss the problem of characterizing all upper homogeneous graded posets with finitely many elements of each rank.