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A102896
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Number of ACI algebras (or semilattices) on n generators with no annihilator.
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7
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OFFSET
| 0,2
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COMMENTS
| Or, number of Moore families on an n-set, that is, families of subsets that contain the universal set {1,...,n} and are closed under intersection.
Or, number of closure operators on a set of n elements.
An ACI algebra or semilattice is a system with a single binary, idempotent, commutative and associative operation.
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REFERENCES
| G. Birkhoff, Lattice Theory. American Mathematical Society, Colloquium Publications, Vol. 25, 3rd ed., Providence, RI, 1967.
Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
P. Colomb, A. Irlande and O. Raynaud, Counting of Moore Families for n=7, International Conference on Formal Concept Analysis (2010) [From Pierre Colomb (pierre(AT)colomb.me), Sep 04 2010]
Pierre Colomb, Alexis Irlande, Olivier Raynaud and Yoan Renaud, About the Recursive Decomposition of the lattice of co-Moore Families, http://www.colomb.me/pierre/data/paper/icfca2011.pdf.
M. Habib and L. Nourine, The number of Moore families on n = 6, Discrete Math., 294 (2005), 291-296.
E. H. Moore, Introduction to a Form of General Analysis, AMS Colloquium Publication 2 (1910), pp. 53-80.
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LINKS
| N. Dershowitz, G. S. Huang and M. Harris, Enumeration Problems Related to Ground Horn Theories arXiv:cs/0610054v2 [cs.LO].
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FORMULA
| a(n) = sum( C(n, k)*A102894, k=0..n), where C(n, k) is the binomial coefficient
For asymptotics see A102897.
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CROSSREFS
| Cf. A102894, A102895, A102897, A108798, A193674, A108800, A193675.
Sequence in context: A046846 A111010 A089307 * A088107 A132524 A153694
Adjacent sequences: A102893 A102894 A102895 * A102897 A102898 A102899
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KEYWORD
| nonn,hard,more
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AUTHOR
| Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jan 18 2005
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EXTENSIONS
| N. J. A. Sloane (njas(AT)research.att.com) added a(6) from the Habib et al. reference, May 26 2005
Additional comments from D. E. Knuth, Jul 01, 2005
a(7) from Pierre Colomb (pierre(AT)colomb.me), Sep 04 2010
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