CONE OF FLAG l-VECTORS OF HALF-EULERIAN POSETS OF RANK 5


Extreme rays, given by interval systems:

  (1):  0
  (2): [1,2]
  (3): [2,3]
  (4): [3,4]
  (5): [1,2][3,4]
  (6): [1,4]


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)
  x4 = l(34) 
  x5 = l(1234) 

Flag l-vectors of extremes:

  ( 1) 1  0  0  0  0 
  ( 2) 1 -1  0  0  0 
  ( 3) 1  0 -1  0  0
  ( 4) 1  0  0 -1  0
  ( 5) 1 -1  0 -1  1
  ( 6) 1  0  0  0 -1

Inequalities for the cone:

  (L  1)          +x4    <= 0    
  (L  2)       +x3       <= 0    
  (L  3)    +x2          <= 0    
  (L  4)          +x4+x5 <= 0    
  (L  5)    +x2      +x5 <= 0    
  (L  6) -x1-x2-x3-x4-x5 <= 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     6 | #
  E \ T  |         |
   Q \ S |         |
    S \  |         |
       \ |         |
-----------------------
1        | ***.. * :  4
2        | **.** * :  5
3        | *.**. * :  4
4        | ***.* . :  4
5        | *.*** . :  4
6        | .**** * :  5
          .............
#        | 54544 4