1, 2, 13, 171, 3994, 154303, 9415189, 878222530,...
https://en.wikipedia.org/wiki/Transitive_relation#Counting_transitive_relations
https://www.quora.com/How-do-I-find-number-of-transitive-relations-on-a-set
On the basis of given link,
There is No general formula to counts the number of transitive relations on a finite set.
a) n=1, number of transitive relations will be 2
b) n=2, number of transitive relations will be 13
There are direct formulas to count other types of relations.
No. of relations =2mn No. of reflexive relations =2 n(n-1) No. of irreflexive relations = 2 n(n-1) No. of symmetric relations = 2 n(n+1)/2 No. of asymmetric relations = 3 n(n-1)/2 No. of Anti Symmetric Relations = 2 n * 3 n(n-1)/2
No. of relations =2mn
No. of reflexive relations =2 n(n-1)
No. of irreflexive relations = 2 n(n-1)
No. of symmetric relations = 2 n(n+1)/2
No. of asymmetric relations = 3 n(n-1)/2
No. of Anti Symmetric Relations = 2 n * 3 n(n-1)/2
I hope te answer is helpful :)
https://cs.uwaterloo.ca/journals/JIS/VOL7/Pfeiffer/pfeiffer6.pdf Please refer to this paper. first take 2 elements (pair) at a time and then take 3 elements ata time in sequence to form transitive relation.
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