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(2010) Formal concept analysis, Dordrecht, Springer.
Given a set U n = {0,1,...,n − 1}, a collection (mathcal{M}) of subsets of U n that is closed under intersection and contains U n is known as a Moore family. The set of Moore families for a given n, denoted by M n , increases very quickly with n, thus |M 3| is 61 and |M 4| is 2480. In [1] the authors determined the number for n = 6 and stated a 24h- computation-time. Thus, the number for n = 7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for n = 7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.
Publication details
DOI: 10.1007/978-3-642-11928-6_6
Full citation:
Colomb, P. , Irlande, A. , Raynaud, O. (2010)., Counting of moore families for n=7, in L. Kwuida & B. Sertkaya (eds.), Formal concept analysis, Dordrecht, Springer, pp. 72-87.
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