Enumeration of AG-groupoids. (English) Zbl 1250.20055
Davenport, James H. (ed.) et al., Intelligent computer mathematics. 18th symposium, Calculemus 2011, and 10th international conference, MKM 2011, Bertinoro, Italy, July 18–23, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-22672-4/pbk). Lecture Notes in Computer Science 6824. Lecture Notes in Artificial Intelligence, 1-14 (2011).
Summary: Enumeration and classification of mathematical entities is an important part of mathematical research in particular in finite algebra. For algebraic structures that are more general than groups this task is often only feasible by use of computers due to the sheer number of structures that have to be considered. In this paper we present the enumeration and partial classification of AG-groupoids – groupoids in which the identity \((ab)c=(cb)a\) holds – of up to order 6. The results are obtained with the help of the computer algebra system GAP and the constraint solver Minion by making use of both algebraic techniques as well as search pruning via symmetry breaking.
For the entire collection see [Zbl 1218.68014].
For the entire collection see [Zbl 1218.68014].
MSC:
| 20N02 | Sets with a single binary operation (groupoids) |
| 05A15 | Exact enumeration problems, generating functions |
| 05B15 | Orthogonal arrays, Latin squares, Room squares |
| 68W30 | Symbolic computation and algebraic computation |
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