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The monoids of orders eight, nine & ten

  • Andreas Distler
  • Tom Kelsey
Article

Abstract

We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and anti-isomorphism, there are 858,977 monoids of order eight; 1,844,075,697 monoids of order nine and 52,991,253,973,742 monoids of order ten.

Keywords

Monoids Enumeration combinatorics AI search 

Mathematics Subject Classifications (2000)

Primary 05E15 Secondary 05-04 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, Mathematical InstituteUniversity of St AndrewsSt AndrewsUK
  2. 2.School of Computer Science, Jack Cole BuildingUniversity of St AndrewsSt AndrewsUK

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