#This file contains all the data needed to show $\pi_{cv}(B_3^-)$ is at most 2/3 (see Section
#2.5.3). The calculation can be verified using the program "HypercubeVertexDensityChecker".

#This file follows a similar format to those created for "DensityChecker". It has been
#commented to highlight the differences.

Program : HypercubeVertexDensityChecker

#Instead of setting the order we instead the dimension of the hypercubes.
#The current implementation of HypercubeEdgeDensityChecker can only handle hypercubes of
#dimension at most 5.
Dimension of subcubes H : 4

#Description of the forbidden family $\mathcal{F}$. Note that a red-blue vertex-coloured 
#hypercube is represented by a sequence of ones and zeros. We assume its vertices are
#labelled 0,1,...,2^n-1 such that ij is an edge if and only if i differs from j by precisely
#one digit in their binary representations. The sequence of ones and zeros represent the
#colours of vertices 2^n-1,...,3,2,1,0 respectively, where a value of one indicates blue
#and zero indicates red.
Number of forbidden hypercubes : 1
Forbidden hypercubes           :
01111111

Number of terms : 5


--- Term 1 ---

#We need only define the dimension of the type. The colouring  of its vertices can be
#determined from the flags (see term 2 for an example).
Dimension of type : 0

Number of flags  : 3
Matrix dimension : 2

#The labelled vertices of the flag (which describe the type) are the vertices 0,...,
#2^"dimension of type"-1. In this case there is only one labelled vertex: the vertex 0.
#Note that the dimension of the flags should be at most
#("dimension of type" + "dimension of subcubes H")/2.
Flags :
F1 : 1100
F2 : 0110
F3 : 1110

Basis :
B1 : (F1)
B2 : (F2)-(F3)

Matrix :
 436/900 -208/900
-208/900  100/900


--- Term 2 ---

Dimension of type : 2
Number of flags   : 4
Matrix dimension  : 2

#The dimension of the type is 2, hence the labelled vertices are 0,1,2,3. By looking at flag
#"F1" we can determine the type has vertices 0 and 1 coloured red, and vertices 2 and 3 blue.

Flags :
F1 : 01101100
F2 : 01111100
F3 : 10011100
F4 : 10111100

Basis :
B1 : (F1)-(F3)
B2 : (F2)-(F4)

Matrix :
  910/900 -1003/900
-1003/900  1175/900 


--- Term 3 ---

Dimension of type : 2
Number of flags   : 7
Matrix dimension  : 4

Flags :
F1 : 00011110
F2 : 00111110
F3 : 01011110
F4 : 01101110
F5 : 10111110
F6 : 11011110
F7 : 11101110

Basis :
B1 : (F1)
B2 : (F2)+(F3)-(F5)-(F6)
B3 : (F4)
B4 : (F7)

Matrix :
 1247/900   580/900  2627/900 -1300/900
  580/900   603/900  2779/900 -1008/900
 2627/900  2779/900 12833/900 -4629/900
-1300/900 -1008/900 -4629/900  2239/900


--- Term 4 ---

Dimension of type : 2
Number of flags   : 8
Matrix dimension  : 3

Flags :
F1 : 00101110
F2 : 00111110
F3 : 01001110
F4 : 01011110
F5 : 10101110
F6 : 10111110
F7 : 11001110
F8 : 11011110

Basis :
B1 : (F1)-(F3)
B2 : (F2)-(F4)+(F6)-(F8)
B3 : (F5)-(F7)

Matrix :
2845/900 1124/900 1062/900
1124/900 3404/900 4149/900
1062/900 4149/900 7817/900


--- Term 5 ---

Dimension of type : 2
Number of flags   : 6
Matrix dimension  : 3

Flags :
F1 : 00011111
F2 : 00101111
F3 : 01011111
F4 : 01101111
F5 : 10011111
F6 : 10101111

Basis :
B1 : (F1)-(F2)
B2 : (F3)-(F6)
B3 : (F4)-(F5)

Matrix :
1449/900 -106/900 1050/900
-106/900 1016/900  -77/900
1050/900  -77/900 1000/900

