Template:Families of Boolean functions/sharpness/possible bijections

possible bijections

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. This leaves a bijection from sharp families to diploid blunt families. From the union of sharp and haploid families to super-families.    Haploid families are themselves complete super-families. So they are assigned to themselves. This leaves a bijection from sharp families to diploid super-families – which include sharp super-families. 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. This seems silly. There is probably no meaningful bijection of this kind.

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compare {{Families of Boolean functions/sharpness/sharp to diploid blunt}}