Combinatorics Seminar

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 Vts 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.

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