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The Number of Semigroups of Order $n$

Daniel J. Kleitman, Bruce R. Rothschild and Joel H. Spencer
Proceedings of the American Mathematical Society
Vol. 55, No. 1 (Feb., 1976), pp. 227-232
DOI: 10.2307/2041879
Stable URL: http://www.jstor.org/stable/2041879
Page Count: 6
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The Number of Semigroups of Order $n$
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Abstract

The number of semigroups on $n$ elements is counted asymptotically for large $n$. It is shown that "almost all" semigroups on $n$ elements have the following property: The $n$ elements are split into sets $A, B$ and there is an $e \in B$ so that whenever $x, y \in A, xy \in B$, but if $x$ or $y$ is in $B, xy = e$.

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