CONE OF SPARSE f-VECTORS OF HALF-EULERIAN POSETS OF RANK 4


Extreme rays, given by interval systems:

   (1): empty family
   (2): [1,2]
   (3): [2,3]

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)
   x3  = f(2)


Sparse flag f-vectors of extremes:

  ( 1) 1 1 1 
  ( 2) 0 1 1 
  ( 3) 0 0 1 

Inequalities for the cone:

  (F  1) -x1       <= 0    
  (F  2)    +x2-x3 <= 0    
  (F  3) +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        | .** :  2
2        | **. :  2
3        | *.* :  2
          .........
#        | 222