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Sets depending on a variable

I'm working on an algorithm that takes as impit a set and works accordingly to the set cardinality. In it I would like to define several sets with different properties in a way similar to this

For n in len(S) : Kn=stuff

However we all know the above will create a single set called Kn and work on it whilst I would like to have a set for each n, how can I do it?

Sets depending on a variable

I'm working on an algorithm that takes as impit a set and works accordingly to the set cardinality. In it I would like to define several sets with different properties in a way similar to this

For n in len(S) : Kn=stuff

However we all know the above will create a single set called Kn and work on it whilst I would like to have a set for each n, how can I do it? it?

This sets will be the base for several other sub algorithm so I need them to extually be defined, it's not enough to have them exist inside a given cycle as I think I should be able to do