How to find out the total number of transitive relations in a set of n elements? I am facing a problem in finding all the possible cases, is it not possible to find all cases? If not possible, why?
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Values are given in http://oeis.org/A006905 No formula is given and only terms up to $n=18$ are given. – Ross Millikan Jan 29 '14 at 14:10
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Wikipedia claims that no general formula that counts transitive relations is known.
Of course, for any particular $n$ you can just find all of them by brute force, but that may take a lot of effort even for smallish $n$s -- even for four elements there are thousands of possible transitive relations.
hmakholm left over Monica
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Can we state why no formula exists without any reference to Wikipedia? – user3209588 Jan 29 '14 at 14:06
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2@user3209588: As far as I know, we can't state that no formula exists, with or without reference to Wikipedia -- just that none is known. – hmakholm left over Monica Jan 29 '14 at 14:10