A285051 - OEIS

%I #13 Aug 07 2017 21:28:45

%S 1,11,268,13705,1122726

%N Idempotent equivalence class multiplications for the full transformation semigroup.

%C Over all n^n transformations create a list of 3-tuples (a,b,c) where a*b = c. For each tuple map each of the three elements to its idempotent under self-composition, (g^i)*(g^i) = g^i. Collect the unique 3-tuples.

%e For n=2: [([0,0],[0,0],[0,0]),([0,0],[0,1],[0,0]),([0,0],[1,1],[0,0]),([0,1],[0,0],[0,0]),([0,1],[0,1],[0,1]),([0,1],[1,1],[1,1]),([0,1],[0,0],[1,1]),([0,1],[1,1],[0,0]),([1,1],[0,0],[1,1]),([1,1],[0,1],[1,1]),([1,1],[1,1],[1,1])]

%K nonn,more

%O 1,2

%A _Chad Brewbaker_, Apr 08 2017