The Smallsemi package is a data library of semigroups of small size. It provides all semigroups with at most 8 elements as well as various information about these objects. The reason that semigroups of higher orders are not included is the huge number of such objects. The numbers of semigroups of sizes 1 to 9 are given in the table below (orders not included in the library are in italics). The number of semigroups of size 10 is not known at the time of writing.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Jonušas, Julius; Troscheit, Sascha: Random ubiquitous transformation semigroups (2019)
  2. Malandro, Martin E.: Enumeration of finite inverse semigroups (2019)
  3. C. Inostroza, I. Kondrashuk, N. Merino, F. Nadal: A Java library to perform S-expansions of Lie algebras (2017) arXiv
  4. Bailey, Alex; Finn-Sell, Martin; Snocken, Robert: Subsemigroup, ideal and congruence growth of free semigroups (2016)
  5. Lee, Edmond W. H.; Li, Jian Rong: The variety generated by all monoids of order four is finitely based. (2015)
  6. Distler, Andreas: Finite nilpotent semigroups of small coclass. (2014)
  7. Distler, Andreas; Kelsey, Tom: The semigroups of order 9 and their automorphism groups. (2014)
  8. Gajdoš, Petr; Kuřil, Martin: Ordered semigroups of size at most 7 and linearly ordered semigroups of size at most 10. (2014)
  9. Distler, Andreas; Eick, Bettina: Coclass theory for nilpotent semigroups via their associated algebras. (2013)
  10. Lee, Edmond W. H.: Finite basis problem for semigroups of order five or less: generalization and revisitation. (2013)
  11. Distler, Andreas; Mitchell, J. D.: The number of nilpotent semigroups of degree 3. (2012)
  12. Distler, Andreas; Shah, Muhammad; Sorge, Volker: Enumeration of AG-groupoids. (2011)
  13. Lee, Edmond W. H.; Li, Jian Rong: Minimal non-finitely based monoids. (2011)
  14. Araújo, J.; Bünau, P. V.; Mitchell, J. D.; Neunhöffer, M.: Computing automorphisms of semigroups. (2010)
  15. Distler, Andreas: Classification and enumeration of finite semigroups. (2010)
  16. Distler, Andreas; Kelsey, Tom: The monoids of orders eight, nine & ten. (2009)
  17. Distler, Andreas; Kelsey, Tom: The monoids of order eight and nine (2008)