### 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 ∈ B so that whenever x, y ∈ A, xy ∈ B, but if x oty is in B, xy = e.

Original language | English (US) |
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Pages (from-to) | 227-232 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1976 |

### Keywords

- Asymptotic enumeration
- Semigroup

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Kleitman, D. J., Rothschild, B. R., & Spencer, J. H. (1976). The number of semigroups of order n.

*Proceedings of the American Mathematical Society*,*55*(1), 227-232. https://doi.org/10.1090/S0002-9939-1976-0414380-0