for a description of the Herzog-Kuhl equations.
i1 : makePureBettiDiagram{0,2,4,5}
0 1 2 3
o1 = total: 3 10 15 8
0: 3 . . .
1: . 10 . .
2: . . 15 8
o1 : BettiTally
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i2 : makePureBettiDiagram({0,2,4,5}, TableEntries => HerzogKuhl)
0 1 2 3
o2 = total: 1/40 1/12 1/8 1/15
0: 1/40 . . .
1: . 1/12 . .
2: . . 1/8 1/15
o2 : BettiTally
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i3 : makePureBettiDiagram{0,3,4,5,6,7,10}
0 1 2 3 4 5 6
o3 = total: 1 50 175 252 175 50 1
0: 1 . . . . . .
1: . . . . . . .
2: . 50 175 252 175 50 .
3: . . . . . . .
4: . . . . . . 1
o3 : BettiTally
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i4 : makePureBettiDiagram({0,3,4,5,6,7,10}, TableEntries => RealizationModules)
0 1 2 3 4 5 6
o4 = total: 36 1800 6300 9072 6300 1800 36
0: 36 . . . . . .
1: . . . . . . .
2: . 1800 6300 9072 6300 1800 .
3: . . . . . . .
4: . . . . . . 36
o4 : BettiTally
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i5 : makePureBettiDiagram{0,3,4,5,6,7,8,11}
0 1 2 3 4 5 6 7
o5 = total: 1 77 330 616 616 330 77 1
0: 1 . . . . . . .
1: . . . . . . . .
2: . 77 330 616 616 330 77 .
3: . . . . . . . .
4: . . . . . . . 1
o5 : BettiTally
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i6 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => HerzogKuhl)
0 1 2 3 4 5 6 7
o6 = total: 1/221760 1/2880 1/672 1/360 1/360 1/672 1/2880 1/221760
0: 1/221760 . . . . . . .
1: . . . . . . . .
2: . 1/2880 1/672 1/360 1/360 1/672 1/2880 .
3: . . . . . . . .
4: . . . . . . . 1/221760
o6 : BettiTally
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i7 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => RealizationModules)
0 1 2 3 4 5 6 7
o7 = total: 45 3465 14850 27720 27720 14850 3465 45
0: 45 . . . . . . .
1: . . . . . . . .
2: . 3465 14850 27720 27720 14850 3465 .
3: . . . . . . . .
4: . . . . . . . 45
o7 : BettiTally
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