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A108798 Number of nonisomorphic systems enumerated by A102894; that is, the number of inequivalent closure operators in which the empty set is closed. Also, the number of union-closed sets with n elements that contain the universe and the empty set.

%I A108798 #39 Dec 19 2023 13:41:18
%S A108798 1,1,3,14,165,14480,108281182,2796163091470050
%N A108798 Number of nonisomorphic systems enumerated by A102894; that is, the number of inequivalent closure operators in which the empty set is closed. Also, the number of union-closed sets with n elements that contain the universe and the empty set.
%C A108798 Also the number of unlabeled finite sets of subsets of {1..n} that contain {} and {1..n} and are closed under intersection. - _Gus Wiseman_, Aug 02 2019
%H A108798 Maria Paola Bonacina and Nachum Dershowitz, <a href="https://doi.org/10.1007/978-3-642-37651-1_3">Canonical ground Horn theories</a>, Lecture Notes in Computer Science 7797, 35-71 (2013).
%H A108798 G. Brinkmann and R. Deklerck, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Brinkmann/brink6.html">Generation of Union-Closed Sets and Moore Families</a>, Journal of Integer Sequences, Vol.21 (2018), Article 18.1.7.
%H A108798 G. Brinkmann and R. Deklerck, <a href="https://arxiv.org/abs/1701.03751">Generation of Union-Closed Sets and Moore Families</a>, arXiv:1701.03751 [math.CO], 2017.
%H A108798 Christopher S. Flippen, <a href="https://scholarscompass.vcu.edu/etd/7527/">Minimal Sets, Union-Closed Families, and Frankl's Conjecture</a>, Master's thesis, Virginia Commonwealth Univ., 2023.
%F A108798 a(n) = A108800(n)/2.
%e A108798 From _Gus Wiseman_, Aug 02 2019: (Start)
%e A108798 Non-isomorphic representatives of the a(0) = 1 through a(3) = 14 union-closed sets of sets:
%e A108798   {}  {}{1}  {}{12}        {}{123}
%e A108798              {}{2}{12}     {}{3}{123}
%e A108798              {}{1}{2}{12}  {}{23}{123}
%e A108798                            {}{1}{23}{123}
%e A108798                            {}{3}{23}{123}
%e A108798                            {}{13}{23}{123}
%e A108798                            {}{2}{3}{23}{123}
%e A108798                            {}{2}{13}{23}{123}
%e A108798                            {}{3}{13}{23}{123}
%e A108798                            {}{12}{13}{23}{123}
%e A108798                            {}{2}{3}{13}{23}{123}
%e A108798                            {}{3}{12}{13}{23}{123}
%e A108798                            {}{2}{3}{12}{13}{23}{123}
%e A108798                            {}{1}{2}{3}{12}{13}{23}{123}
%e A108798 (End)
%Y A108798 The labeled version is A102894.
%Y A108798 Cf. A000612, A001930, A003180, A102895, A102897, A108800, A193674, A193675, A326867, A326869, A326883.
%K A108798 nonn,more
%O A108798 0,3
%A A108798 _Don Knuth_, Jul 01 2005
%E A108798 a(6) added (using A193674) by _N. J. A. Sloane_, Aug 02 2011
%E A108798 Added a(7), and reference to union-closed sets. - _Gunnar Brinkmann_, Feb 05 2018