CONE OF FLAG l-VECTORS OF HALF-EULERIAN POSETS OF RANK 3


Extreme rays, given by interval systems:

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

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)

Flag l-vectors of extremes:

  ( 1) 1  0
  ( 2) 1 -1

Inequalities for the cone:

  (L  1)    +x2 <= 0    
  (L  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 (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        | *. :  1
2        | .* :  1
          ........
#        | 11