CONE OF FLAG l-VECTORS OF HALF-EULERIAN POSETS OF RANK 6


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]
  ( 7): [4,5]
  ( 8): [1,2][4,5]
  ( 9): [2,3][4,5]
  (10): [2,5]

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)
  x6 = l(45)
  x7 = l(1245)
  x8 = l(2345)

Flag l-vectors of extremes:

  ( 1) 1  0  0  0  0  0  0  0 
  ( 2) 1 -1  0  0  0  0  0  0 
  ( 3) 1  0 -1  0  0  0  0  0 
  ( 4) 1  0  0 -1  0  0  0  0 
  ( 5) 1 -1  0 -1  1  0  0  0 
  ( 6) 1  0  0  0 -1  0  0  0 
  ( 7) 1  0  0  0  0 -1  0  0 
  ( 8) 1 -1  0  0  0 -1  1  0 
  ( 9) 1  0 -1  0  0 -1  0  1 
  (10) 1  0  0  0  0  0  0 -1 


Inequalities for the cone:

  (L  1)          +x4             <= 0    
  (L  2)       +x3                <= 0    
  (L  3)                +x6+x7    <= 0    
  (L  4)          +x4+x5          <= 0    
  (L  5)       +x3            +x8 <= 0    
  (L  6)    +x2            +x7    <= 0    
  (L  7)                +x6+x7+x8 <= 0    
  (L  8)    +x2      +x5   +x7    <= 0    
  (L  9)                   -x7    <= 0    
  (L 10) -x1-x2-x3-x4-x5-x6-x7-x8 <= 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        | ***.. ***** :  8
2        | **.** ***.* :  8
3        | ***** *.*.* :  8
4        | ***.* .**** :  8
5        | **.** ****. :  8
6        | *.**. ***** :  8
7        | ***** *.**. :  8
8        | *.*** .**** :  8
9        | ***** **.** :  9
10       | .**** ***** :  9
          .................
#        | 98888 88988