What do you mean by "permutation-dependent"? I'm curious, because I write an article about permutations and I'd be happy to introduce some astrology :)
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What I mean is - there are 9 "planets", aka bodies. Each has a specific orbit. Astrology isn't "sun was in that sign on that day", that's like saying programming is C#.
Your sign depends on the each of the planet's position towards the earth sky and towards each other. So two people born on the same day in different years will have vastly different horoscopes.