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!
 
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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> 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Adin   <radin@math.biu.ac.il>