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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of semigroups of order $ n$


Authors: Daniel J. Kleitman, Bruce R. Rothschild and Joel H. Spencer
Journal: Proc. Amer. Math. Soc. 55 (1976), 227-232
MSC: Primary 05A15; Secondary 20M99
MathSciNet review: 0414380
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0414380-0
PII: S 0002-9939(1976)0414380-0
Keywords: Semigroup, asymptotic enumeration
Article copyright: © Copyright 1976 American Mathematical Society