The Monoids of Order Eight and Nine

Research output: Contribution to conferencePaperpeer-review

8 Citations (Scopus)


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 9 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 8 and 1,844,075,697 monoids of order 9.
Original languageEnglish
Publication statusPublished - Jul 2008


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