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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)

Abstract

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.

Keywords

Canonical Form Hash Table Closure Operator Formal Concept Analysis Integer Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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