Counting of Moore Families for n=7

  • Pierre Colomb
  • Alexis Irlande
  • Olivier Raynaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5986)


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.


Canonical Form Hash Table Closure Operator Formal Concept Analysis Integer Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pierre Colomb
    • 1
  • Alexis Irlande
    • 2
  • Olivier Raynaud
    • 1
  1. 1.Université Blaise PascalAubiéreFrance
  2. 2.Universidad Nacional de ColombiaBogotaColombia

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