The number of semigroups of order n

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)227-232
Number of pages6
JournalProceedings of the American Mathematical Society
Volume55
Issue number1
DOIs
StatePublished - 1976

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Semigroup

Keywords

  • Asymptotic enumeration
  • Semigroup

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 55, No. 1, 1976, p. 227-232.

Research output: Contribution to journalArticle

Kleitman, Daniel J. ; Rothschild, Bruce R. ; Spencer, Joel. / The number of semigroups of order n. In: Proceedings of the American Mathematical Society. 1976 ; Vol. 55, No. 1. pp. 227-232.
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