The Monoids of Order Eight and Nine

Authors:
Andreas Distler;Tom Kelsey
Affiliations:
School of Mathematics and Statistics, Mathematical Institute, , UK KY16 9SS;School of Computer Science, Jack Cole Building, , UK KY16 9SX
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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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 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.