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ideed
Group Title
How many equivalence relations are there in a set of n elements...?
 one year ago
 one year ago
ideed Group Title
How many equivalence relations are there in a set of n elements...?
 one year ago
 one year ago

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KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
Have you learned much about set partitions?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
i think this is not easy it is identical to asking how many partitions there are. maybe i am mistaken, but i don't think this has an obvious answer
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
a quick google search finds these are bell numbers https://oeis.org/A000110
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
or scroll down to "counting possible partitions" here http://en.wikipedia.org/wiki/Equivalence_relation
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
It's actually rather straightforward to figure this out. You can make a bijection between the set of set partitions and the set of equivalence relations on a set of n elements by equating partitions to equivalence classes.
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
To prove this is actually a bijection, just notice that it has an easy inverse (either way you go, just relabel set partitions as equivalence classes and vice versa). Thus, since it has an inverse, it must be bijective.
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
ok, but how do you count them?
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
Well, that's a different story.
 one year ago
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