CONE OF SPARSE f-VECTORS OF HALF-EULERIAN POSETS OF RANK 3


Extreme rays, given by interval systems:

   (1): empty family
   (2): [1,2]

Sparse flag f-vectors
   The entries f(S) in the sparse flag vector are represented by 
   variables xi as follows:

   x1  = f(emptyset)
   x2  = f(1)

Sparse flag f-vectors of extremes:

  ( 1) 1 1 
  ( 2) 0 1 

Inequalities for the cone:

  (F  1) -x1    <= 0    
  (F  2) +x1-x2 <= 0    

Strong validity table.  A * in row i and column j indicates that 
extreme (j) lies on the facet given by inequality (F i).  The 
right-most column gives the number of extremes on each facet.
The bottom two rows, read vertically, give the number of facets
containing each extreme.

\ P      |    |
 \ O     |    |
I \ I    |    |
 N \ N   | 1  | #
  E \ T  |    |
   Q \ S |    |
    S \  |    |
       \ |    |
------------------
1        | .* :  1
2        | *. :  1
          ........
#        | 11