### 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) |
---|---|

Pages (from-to) | 227-232 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - 1976 |

### Fingerprint

### Keywords

- Asymptotic enumeration
- Semigroup

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*55*(1), 227-232. https://doi.org/10.1090/S0002-9939-1976-0414380-0

**The number of semigroups of order n.** / Kleitman, Daniel J.; Rothschild, Bruce R.; Spencer, Joel.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 55, no. 1, pp. 227-232. https://doi.org/10.1090/S0002-9939-1976-0414380-0

}

TY - JOUR

T1 - The number of semigroups of order n

AU - Kleitman, Daniel J.

AU - Rothschild, Bruce R.

AU - Spencer, Joel

PY - 1976

Y1 - 1976

N2 - 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.

AB - 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.

KW - Asymptotic enumeration

KW - Semigroup

UR - http://www.scopus.com/inward/record.url?scp=84966259821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966259821&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1976-0414380-0

DO - 10.1090/S0002-9939-1976-0414380-0

M3 - Article

AN - SCOPUS:84966259821

VL - 55

SP - 227

EP - 232

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -