Template:Families of Boolean functions/sharpness
| possible bijections |
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The quantities suggest two kinds of bijection for arities greater 1: From the union of sharp and haploid families to blunt families.
Haploid families are themselves blunt. So they are assigned to themselves. From the union of sharp and haploid families to super-families.
Haploid families are themselves complete super-families. So they are assigned to themselves. E.g. the light sharp families could be assigned to the super-families containing them, and the heavy sharp families to the diploid blunt super-families. |
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These images show the 32 diploid families for arity 3 within their super-families.
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These images show the 14 haploid (blunt) families for arity 3.
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The twin prefect (prefect of the twin) is the essentially the consul, but refined by a sign. 0 ¬1 ¬2 3 ¬4 5 6 ¬7 |

