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. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Distler, A., & Kelsey, T. (2008). The monoids of order eight and nine. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5144 LNAI, pp. 61–76). https://doi.org/10.1007/978-3-540-85110-3_7
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