The number of semigroups of order 𝑛
Daniel J. Kleitman, Bruce L. Rothschild, Joel Spencer · Proceedings of the American Mathematical Society · 1976
The number of semigroups on n n elements is counted asymptotically for large n n . It is shown that “almost all” semigroups on n n elements have the following property: The n n elements are split into sets A , B A,B and there is an e ∈ B e \in B so that whenever x , y ∈ A , x y ∈ B x,y \in A,xy \in B , but if x x or y y is in B , x y = e B,xy = e .