Bar-Ilan Combinatorics Seminar The next meeting of the seminar will take place, IYH, (when) Sunday, 17 Adar (March 11), 14:00-15:30 (where) Room 201 (Math & CS Seminar Room), Building 216, Bar-Ilan University (who) Eran Nevo (Ben-Gurion University) (what) On flag f-vectors of Gorenstein* posets Abstract: The flag f-vector is a basic invariant of finite graded posets, counting chains according to the set of ranks they occupy. For Eulerian posets it is efficiently encoded by the cd-index, a noncommutative polynomial in variables $c$ and $d$ with integer coefficients. Moreover, if the poset is Gorenstien*, in particular if the order complex of its proper part is topologically a sphere, then Karu proved Stanley's conjecture that all the coefficients of the cd-index are nonnegative. What more can be said about the cd-index of Gorenstein* posets? Upper bounds? A characterization? We characterize the cd-index for rank 5 (lower ranks are easy, rank 5 corresponds to 3-dimensional spheres), obtain upper bounds for certain coefficients in all ranks, and conjecture further upper bounds for the entire cd-index. Reflects joint with Satoshi Murai. All needed background will be given in the talk! ************************************************************************* You are all invited! Graduate students are especially welcome. Seminar organizer: Ron Adin <radin@math.biu.ac.il> Seminar's homepage: <http://www.math.biu.ac.il/~radin/comsem/comsem.html> ************************************************************************* --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Adin <radin@math.biu.ac.il>