CONE OF FLAG l-VECTORS OF HALF-EULERIAN POSETS OF RANK 4


Extreme rays, given by interval systems:

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

Flag l-vectors

  The entries l(S) in the flag l-vector are represented by 
  variables xi as follows:

  x1 = l(emptyset)
  x2 = l(12)
  x3 = l(23)

Flag l-vectors of extremes:

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

Inequalities for the cone:

  (L  1)       +x3 <= 0    
  (L  2)    +x2    <= 0    
  (L  3) -x1-x2-x3 <= 0    

Strong validity table. A * in row i and column j indicates that 
extreme (j) lies on the facet given by inequality (L 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