A285051 Idempotent equivalence class multiplications for the full transformation semigroup.

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Offset: 1

Author

Chad Brewbaker, Apr 08 2017

Keywords

• nonn
• more

Comments

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.

Examples

			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])]