The number of semigroups of order n

Daniel J. Kleitman, Bruce R. Rothschild, Joel H. Spencer

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)227-232
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Feb 1976


  • Asymptotic enumeration
  • Semigroup

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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