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.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Lee, Edmond W.H.; Li, Jian Rong: The variety generated by all monoids of order four is finitely based. (2015)
- Distler, Andreas; Kelsey, Tom: The semigroups of order 9 and their automorphism groups. (2014)
- Gajdoš, Petr; Kuřil, Martin: Ordered semigroups of size at most 7 and linearly ordered semigroups of size at most 10. (2014)
- Lee, Edmond W.H.: Finite basis problem for semigroups of order five or less: generalization and revisitation. (2013)
- Distler, Andreas; Mitchell, J.D.: The number of nilpotent semigroups of degree 3. (2012)
- Lee, Edmond W.H.; Li, Jian Rong: Minimal non-finitely based monoids. (2011)
- Distler, Andreas: Classification and enumeration of finite semigroups. (2010)
- Distler, Andreas; Kelsey, Tom: The monoids of orders eight, nine & ten. (2009)