A193675
Number of nonisomorphic systems enumerated by A102897; that is, the number of inequivalent Horn functions, under permutation of variables.
Original entry on oeis.org
2, 4, 10, 38, 368, 29328, 216591692, 5592326399531792
Offset: 0
From _Gus Wiseman_, Aug 04 2019: (Start)
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)
- D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
The same with intersection instead of union is also
A193675.
The case closed under both union and intersection also is
A326908.
a(6) corrected by Pierre Colomb, Aug 02 2011
A326906
Number of sets of subsets of {1..n} that are closed under union and cover all n vertices.
Original entry on oeis.org
2, 2, 8, 90, 4542, 2747402, 151930948472, 28175295407840207894
Offset: 0
The a(0) = 2 through a(2) = 8 sets of subsets:
{} {{1}} {{1,2}}
{{}} {{},{1}} {{},{1,2}}
{{1},{1,2}}
{{2},{1,2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
The case without empty sets is
A102894.
The case with a single covering edge is
A102895.
The case also closed under intersection is
A326878 for n > 0.
The same for intersection instead of union is (also)
A326906.
-
Table[Length[Select[Subsets[Subsets[Range[n]]],Union@@#==Range[n]&&SubsetQ[#,Union@@@Tuples[#,2]]&]],{n,0,3}]
A326942
Number of unlabeled T_0 sets of subsets of {1..n} that cover all n vertices.
Original entry on oeis.org
2, 2, 6, 58, 3770
Offset: 0
Non-isomorphic representatives of the a(0) = 2 through a(2) = 6 sets of subsets:
{} {{1}} {{1},{2}}
{{}} {{},{1}} {{2},{1,2}}
{{},{1},{2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
The case without empty edges is
A319637.
The non-covering version is
A326949 (partial sums).
Cf.
A000371,
A003180,
A055621,
A059201,
A316978,
A319559,
A319564,
A326907,
A326941,
A326943,
A326946.
A326909
Number of sets of subsets of {1..n} closed under union and intersection and covering all of the vertices.
Original entry on oeis.org
2, 2, 7, 45, 500, 9053, 257151, 11161244, 725343385, 69407094565, 9639771895398, 1919182252611715, 541764452276876719, 214777343584048313318, 118575323291814379721651, 90492591258634595795504697, 94844885130660856889237907260, 135738086271526574073701454370969, 263921383510041055422284977248713291
Offset: 0
The a(0) = 2 through a(2) = 7 sets of subsets:
{} {{1}} {{1,2}}
{{}} {{},{1}} {{},{1,2}}
{{1},{1,2}}
{{2},{1,2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{},{1},{2},{1,2}}
Covering sets of subsets are
A000371.
The case without empty sets is
A108798.
The case with a single covering edge is
A326878.
The unlabeled version is
A326898 for n > 0.
The case closed only under union is
A326906.
The case closed only under intersection is (also)
A326906.
-
Table[Length[Select[Subsets[Subsets[Range[n]]],Union@@#==Range[n]&&SubsetQ[#,Union[Union@@@Tuples[#,2],Intersection@@@Tuples[#,2]]]&]],{n,0,3}]
(* Second program: *)
A000798 = Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {, }][[All, 2]];
A006058 = Cases[Import["https://oeis.org/A006058/b006058.txt", "Table"], {, }][[All, 2]];
a[n_] := A006058[[n + 1]] + A000798[[n + 1]];
a /@ Range[0, 18] (* Jean-François Alcover, Dec 30 2019 *)
Showing 1-4 of 4 results.
Comments