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A193675
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Number of nonisomorphic systems enumerated by A102897; that is, the number of inequivalent Horn functions, under permutation of variables.
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16
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OFFSET
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0,1
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COMMENTS
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When speaking of inequivalent Boolean functions, three groups of symmetries are typically considered: Complementations only, the Abelian group (2,...,2) of 2^n elements; permutations only, the symmetric group of n! elements; or both complementations and permutations, the octahedral group of 2^n n! elements. In this case only symmetry with respect to the symmetric group is appropriate because complementation affects the property of being a Horn function.
Also the number of non-isomorphic sets of subsets of {1..n} that are closed under union. - Gus Wiseman, Aug 04 2019
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
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LINKS
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FORMULA
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EXAMPLE
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Non-isomorphic representatives of the a(0) = 2 through a(2) = 10 sets of sets:
{} {} {}
{{}} {{}} {{}}
{{1}} {{1}}
{{},{1}} {{1,2}}
{{},{1}}
{{},{1,2}}
{{2},{1,2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
(End)
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CROSSREFS
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The same with intersection instead of union is also A193675.
The case closed under both union and intersection also is A326908.
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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EXTENSIONS
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a(6) corrected by Pierre Colomb, Aug 02 2011
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STATUS
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approved
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