#Density : 3/16

Program                      : VertexInducedHypercubeDensityChecker

Dimension of subcubes H      : 4
Number of induced hypercubes : 1
Induced hypercubes           :
4 : {5, 6, 8, 11, 12, 13, 14, 15}
Number of terms              : 17


--- Term 1 ---

Dimension of type  : 0
Dimension of flags : 2
Number of flags    : 6
Matrix dimension   : 3

Flags :
F1 : {0}
F2 : {0, 2}
F3 : {0, 3}
F4 : {0, 2, 3}
F5 : {0, 1, 2}
F6 : {0, 1, 2, 3}

Basis :
B1 : 45(F1)-8(F2)-25(F3)-12(F4)+11(F5)+9(F6)
B2 : 3(F1)+4(F2)+4(F3)-11(F4)+3(F5)+4(F6)
B3 : 11(F1)-8(F2)+9(F3)-12(F4)+45(F5)-25(F6)

Matrix :
8890431422383/32088932352000000 12599093499463/32088932352000000 12970797921197/64177864704000000
12599093499463/32088932352000000 216744039719/100277913600000 15890558633353/32088932352000000
12970797921197/64177864704000000 15890558633353/32088932352000000 1421743/4624000000


--- Term 2 ---

Dimension of type  : 0
Dimension of flags : 2
Number of flags    : 6
Matrix dimension   : 3

Flags :
F1 : {}
F2 : {2}
F3 : {3}
F4 : {2, 3}
F5 : {1, 2}
F6 : {1, 2, 3}

Basis :
B1 : 4(F1)-11(F2)+3(F3)+4(F4)+4(F5)+3(F6)
B2 : 25(F1)+12(F2)-45(F3)+8(F4)-9(F5)-11(F6)
B3 : 9(F1)-12(F2)+11(F3)-8(F4)-25(F5)+45(F6)

Matrix :
27092989397/12534739200000 -15890565783713/32088932352000000 12599094315551/32088932352000000
-15890565783713/32088932352000000 5227/17000000 -518831340937/2567114588160000
12599094315551/32088932352000000 -518831340937/2567114588160000 8890438186079/32088932352000000


--- Term 3 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 1

Flags :
F1 : {1}
F2 : {1, 2}
F3 : {1, 3}
F4 : {1, 2, 3}

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

Matrix :
43677/2000000


--- Term 4 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 1

Flags :
F1 : {0, 1}
F2 : {0, 1, 2}
F3 : {0, 1, 3}
F4 : {0, 1, 2, 3}

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

Matrix :
947434854143/55517184000000


--- Term 5 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 1

Flags :
F1 : {}
F2 : {2}
F3 : {3}
F4 : {2, 3}

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

Matrix :
947424273409/55517184000000


--- Term 6 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 8

Flags :
F1  : {3}
F2  : {3, 4}
F3  : {3, 4, 5}
F4  : {3, 4, 6}
F5  : {3, 5, 6}
F6  : {3, 4, 5, 6}
F7  : {3, 7}
F8  : {3, 4, 7}
F9  : {3, 5, 7}
F10 : {3, 6, 7}
F11 : {3, 5, 6, 7}
F12 : {3, 4, 5, 6, 7}

Basis :
B1 : (F2)
B2 : (F3)+(F4)
B3 : (F1)-(F5)
B4 : (F6)
B5 : (F7)
B6 : (F9)+(F10)
B7 : (F11)
B8 : (F8)-(F12)

Matrix :
275599/500000 7677/250000 2819/16000 -79547/500000 -168941/1000000 -140539/1000000 -17477/100000 30837/2000000
7677/250000 10837/25000 390037/2000000 -69891/1000000 -21283/500000 -134401/1000000 -73363/500000 -56517/1000000
2819/16000 390037/2000000 372043/400000 -30397/2000000 209091/2000000 -392283/2000000 -501669/2000000 145587/1000000
-79547/500000 -69891/1000000 -30397/2000000 1314243/1000000 -38113/200000 -1022/15625 -151669/1000000 -186373/1000000
-168941/1000000 -21283/500000 209091/2000000 -38113/200000 1255473/1000000 -92717/1000000 -2723/12500 36003/200000
-140539/1000000 -134401/1000000 -392283/2000000 -1022/15625 -92717/1000000 84173/200000 4107/62500 43799/1000000
-17477/100000 -73363/500000 -501669/2000000 -151669/1000000 -2723/12500 4107/62500 286461/500000 149/200000
30837/2000000 -56517/1000000 145587/1000000 -186373/1000000 36003/200000 43799/1000000 149/200000 1378931/1000000


--- Term 7 ---

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

Flags :
F1 : {3, 5}
F2 : {3, 4, 5}
F3 : {3, 6}
F4 : {3, 4, 6}
F5 : {3, 5, 7}
F6 : {3, 4, 5, 7}
F7 : {3, 6, 7}
F8 : {3, 4, 6, 7}

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

Matrix :
847199/500000 74627/125000 34225101329/108432000000
74627/125000 843323/500000 20021390609/36864000000
34225101329/108432000000 20021390609/36864000000 1179097/500000


--- Term 8 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 8

Flags :
F1  : {2, 3}
F2  : {2, 3, 4}
F3  : {2, 3, 5}
F4  : {2, 3, 4, 5}
F5  : {2, 3, 6}
F6  : {2, 3, 4, 6}
F7  : {2, 3, 5, 6}
F8  : {2, 3, 4, 5, 6}
F9  : {2, 3, 7}
F10 : {2, 3, 4, 7}
F11 : {2, 3, 5, 7}
F12 : {2, 3, 4, 5, 7}
F13 : {2, 3, 6, 7}
F14 : {2, 3, 4, 6, 7}
F15 : {2, 3, 5, 6, 7}
F16 : {2, 3, 4, 5, 6, 7}

Basis :
B1 : (F1)
B2 : (F2)+(F3)
B3 : (F5)+(F9)
B4 : (F7)+(F10)
B5 : (F8)+(F12)
B6 : (F4)-(F6)-(F11)+(F13)
B7 : (F14)+(F15)
B8 : (F16)

Matrix :
652861/500000 26223/1000000 -69143/500000 -21387/1000000 -5731/500000 -460849/1500000 -170537/1000000 -165673/500000
26223/1000000 1700649/1000000 -1235487/1000000 -42259/200000 257549/250000 73583/1500000 -1184517/1000000 -1433/125000
-69143/500000 -1235487/1000000 1541677/1000000 27489/1000000 -1184519/1000000 66229/3000000 1025171/1000000 -170537/1000000
-21387/1000000 -42259/200000 27489/1000000 108809/200000 -42259/200000 -109547/750000 27489/1000000 -10693/500000
-5731/500000 257549/250000 -1184519/1000000 -42259/200000 106291/62500 147161/3000000 -308873/250000 1639/62500
-460849/1500000 73583/1500000 66229/3000000 -109547/750000 147161/3000000 88597/120000 66227/3000000 -9601/31250
-170537/1000000 -1184517/1000000 1025171/1000000 27489/1000000 -308873/250000 66227/3000000 1541681/1000000 -138287/1000000
-165673/500000 -1433/125000 -170537/1000000 -10693/500000 1639/62500 -9601/31250 -138287/1000000 1305723/1000000


--- Term 9 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 10
Matrix dimension   : 5

Flags :
F1  : {2, 3, 4}
F2  : {2, 3, 5}
F3  : {2, 3, 6}
F4  : {2, 3, 5, 6}
F5  : {2, 3, 4, 5, 6}
F6  : {2, 3, 7}
F7  : {2, 3, 4, 7}
F8  : {2, 3, 4, 5, 7}
F9  : {2, 3, 4, 6, 7}
F10 : {2, 3, 5, 6, 7}

Basis :
B1 : (F1)-(F2)
B2 : (F3)-(F6)
B3 : (F4)-(F7)
B4 : (F5)-(F8)
B5 : (F9)-(F10)

Matrix :
452657/200000 84507/50000 -10933/250000 311477/200000 102691/62500
84507/50000 1253079/500000 3679/62500 1643059/1000000 1621841/1000000
-10933/250000 3679/62500 146381/125000 43733/1000000 -58861/1000000
311477/200000 1643059/1000000 43733/1000000 452657/200000 338027/200000
102691/62500 1621841/1000000 -58861/1000000 338027/200000 2506151/1000000


--- Term 10 ---

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

Flags :
F1 : {1, 2}
F2 : {1, 2, 4, 5}
F3 : {1, 2, 4, 6}
F4 : {1, 2, 5, 6}
F5 : {1, 2, 4, 7}
F6 : {1, 2, 5, 7}
F7 : {1, 2, 6, 7}
F8 : {1, 2, 4, 5, 6, 7}

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

Matrix :
46067/500000 10721/400000
10721/400000 248807/1600000


--- Term 11 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 7

Flags :
F1  : {1, 2, 4}
F2  : {1, 2, 5}
F3  : {1, 2, 4, 5}
F4  : {1, 2, 6}
F5  : {1, 2, 4, 6}
F6  : {1, 2, 4, 5, 6}
F7  : {1, 2, 7}
F8  : {1, 2, 5, 7}
F9  : {1, 2, 4, 5, 7}
F10 : {1, 2, 6, 7}
F11 : {1, 2, 4, 6, 7}
F12 : {1, 2, 5, 6, 7}

Basis :
B1 : (F1)-(F7)
B2 : (F2)-(F4)
B3 : (F3)-(F5)
B4 : (F3)-(F8)
B5 : (F3)-(F10)
B6 : (F6)-(F12)
B7 : (F9)-(F11)

Matrix :
1888089569/2259000000 0/1 -42879/200000 42879/200000 42879/200000 21521/500000 0/1
0/1 1187453/1000000 12143/250000 -12143/250000 12143/250000 0/1 21521/500000
-42879/200000 12143/250000 1284419/1000000 -328183/1000000 -478117/1000000 -12143/250000 42879/200000
42879/200000 -12143/250000 -328183/1000000 1284419/1000000 -239059/500000 12143/250000 -42879/200000
42879/200000 12143/250000 -478117/1000000 -239059/500000 1284419/1000000 12143/250000 42879/200000
21521/500000 0/1 -12143/250000 12143/250000 12143/250000 3296200440013/2775859200000 0/1
0/1 21521/500000 42879/200000 -42879/200000 42879/200000 0/1 3866809669973/4626432000000


--- Term 12 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 8

Flags :
F1  : {1, 2, 3}
F2  : {1, 2, 3, 4}
F3  : {1, 2, 3, 4, 5}
F4  : {1, 2, 3, 4, 6}
F5  : {1, 2, 3, 5, 6}
F6  : {1, 2, 3, 4, 5, 6}
F7  : {1, 2, 3, 7}
F8  : {1, 2, 3, 4, 7}
F9  : {1, 2, 3, 5, 7}
F10 : {1, 2, 3, 6, 7}
F11 : {1, 2, 3, 5, 6, 7}
F12 : {1, 2, 3, 4, 5, 6, 7}

Basis :
B1 : (F2)
B2 : (F3)+(F4)
B3 : (F1)-(F5)
B4 : (F6)
B5 : (F7)
B6 : (F9)+(F10)
B7 : (F11)
B8 : (F8)-(F12)

Matrix :
328559/250000 -17469/250000 46593/250000 -1591/10000 -151673/1000000 -32697/500000 -19057/100000 7599/500000
-17469/250000 8669/20000 14129/250000 96/3125 -146719/1000000 -134433/1000000 -42551/1000000 -195021/1000000
46593/250000 14129/250000 1103143/800000 -30837/2000000 -149/200000 -219/5000 -360029/2000000 72793/500000
-1591/10000 96/3125 -30837/2000000 110239/200000 -174773/1000000 -8783/62500 -84473/500000 -176187/1000000
-151673/1000000 -146719/1000000 -149/200000 -174773/1000000 14323/25000 65721/1000000 -43569/200000 62709/250000
-32697/500000 -134433/1000000 -219/5000 -8783/62500 65721/1000000 105209/250000 -92703/1000000 392283/2000000
-19057/100000 -42551/1000000 -360029/2000000 -84473/500000 -43569/200000 -92703/1000000 627733/500000 -52273/500000
7599/500000 -195021/1000000 72793/500000 -176187/1000000 62709/250000 392283/2000000 -52273/500000 3720431/4000000


--- Term 13 ---

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

Flags :
F1 : {1, 2, 3, 5}
F2 : {1, 2, 3, 4, 5}
F3 : {1, 2, 3, 6}
F4 : {1, 2, 3, 4, 6}
F5 : {1, 2, 3, 5, 7}
F6 : {1, 2, 3, 4, 5, 7}
F7 : {1, 2, 3, 6, 7}
F8 : {1, 2, 3, 4, 6, 7}

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

Matrix :
423599/250000 298509/500000 -157817/500000
298509/500000 33733/20000 -108623/200000
-157817/500000 -108623/200000 9432777/4000000


--- Term 14 ---

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

Flags :
F1 : {0, 1, 2, 3}
F2 : {0, 1, 2, 3, 4, 5}
F3 : {0, 1, 2, 3, 4, 6}
F4 : {0, 1, 2, 3, 5, 6}
F5 : {0, 1, 2, 3, 4, 7}
F6 : {0, 1, 2, 3, 5, 7}
F7 : {0, 1, 2, 3, 6, 7}
F8 : {0, 1, 2, 3, 4, 5, 6, 7}

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

Matrix :
18607/250000 -1004/46875
-1004/46875 186661/2250000


--- Term 15 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 7

Flags :
F1  : {0, 1, 2, 3, 4}
F2  : {0, 1, 2, 3, 5}
F3  : {0, 1, 2, 3, 4, 5}
F4  : {0, 1, 2, 3, 6}
F5  : {0, 1, 2, 3, 4, 6}
F6  : {0, 1, 2, 3, 4, 5, 6}
F7  : {0, 1, 2, 3, 7}
F8  : {0, 1, 2, 3, 5, 7}
F9  : {0, 1, 2, 3, 4, 5, 7}
F10 : {0, 1, 2, 3, 6, 7}
F11 : {0, 1, 2, 3, 4, 6, 7}
F12 : {0, 1, 2, 3, 5, 6, 7}

Basis :
B1 : (F2)-(F4)
B2 : (F1)-(F7)
B3 : (F3)-(F5)
B4 : (F3)-(F8)
B5 : (F3)-(F10)
B6 : (F9)-(F11)
B7 : (F6)-(F12)

Matrix :
3376953/4000000 0/1 62937/1000000 -62937/1000000 62937/1000000 20711/500000 0/1
0/1 422119/500000 -62937/1000000 62937/1000000 62937/1000000 0/1 20711/500000
62937/1000000 -62937/1000000 386839/500000 -327699/1000000 -222989/1000000 165083/2000000 -82541/1000000
-62937/1000000 62937/1000000 -327699/1000000 386839/500000 -222989/1000000 -165083/2000000 82541/1000000
62937/1000000 62937/1000000 -222989/1000000 -222989/1000000 386839/500000 165083/2000000 82541/1000000
20711/500000 0/1 165083/2000000 -165083/2000000 165083/2000000 114213/250000 0/1
0/1 20711/500000 -82541/1000000 82541/1000000 82541/1000000 0/1 140906188453/308428800000


--- Term 16 ---

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

Flags :
F1 : {}
F2 : {4, 5}
F3 : {4, 6}
F4 : {5, 6}
F5 : {4, 7}
F6 : {5, 7}
F7 : {6, 7}
F8 : {4, 5, 6, 7}

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

Matrix :
18607/250000 -21419/1000000
-21419/1000000 186661/2250000


--- Term 17 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 7

Flags :
F1  : {4}
F2  : {5}
F3  : {4, 5}
F4  : {6}
F5  : {4, 6}
F6  : {4, 5, 6}
F7  : {7}
F8  : {5, 7}
F9  : {4, 5, 7}
F10 : {6, 7}
F11 : {4, 6, 7}
F12 : {5, 6, 7}

Basis :
B1 : (F2)-(F4)
B2 : (F1)-(F7)
B3 : (F3)-(F5)
B4 : (F3)-(F8)
B5 : (F3)-(F10)
B6 : (F9)-(F11)
B7 : (F6)-(F12)

Matrix :
114213/250000 0/1 165083/2000000 -165083/2000000 165083/2000000 16569/400000 0/1
0/1 8256230701/18072000000 -82541/1000000 82541/1000000 82541/1000000 0/1 20711/500000
165083/2000000 -82541/1000000 773679/1000000 -327701/1000000 -222989/1000000 1007/16000 -62937/1000000
-165083/2000000 82541/1000000 -327701/1000000 773679/1000000 -222989/1000000 -1007/16000 62937/1000000
165083/2000000 82541/1000000 -222989/1000000 -222989/1000000 773679/1000000 1007/16000 62937/1000000
16569/400000 0/1 1007/16000 -1007/16000 1007/16000 1688477/2000000 0/1
0/1 20711/500000 -62937/1000000 62937/1000000 62937/1000000 0/1 422119/500000

