The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326362 Number of maximal intersecting antichains of nonempty, non-singleton subsets of {1..n}. 12
 1, 1, 1, 2, 16, 163, 11742, 12160640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A set system (set of sets) is an antichain if no part is a subset of any other, and is intersecting if no two parts are disjoint. LINKS Table of n, a(n) for n=0..7. FORMULA For n > 1, a(n) = A326363(n) - n - 1 = A007363(n + 1) - n. EXAMPLE The a(4) = 16 maximal intersecting antichains: {{1,2,3,4}} {{1,2},{1,3},{2,3}} {{1,2},{1,4},{2,4}} {{1,3},{1,4},{3,4}} {{2,3},{2,4},{3,4}} {{1,2},{1,3,4},{2,3,4}} {{1,3},{1,2,4},{2,3,4}} {{1,4},{1,2,3},{2,3,4}} {{2,3},{1,2,4},{1,3,4}} {{2,4},{1,2,3},{1,3,4}} {{3,4},{1,2,3},{1,2,4}} {{1,2},{1,3},{1,4},{2,3,4}} {{1,2},{2,3},{2,4},{1,3,4}} {{1,3},{2,3},{3,4},{1,2,4}} {{1,4},{2,4},{3,4},{1,2,3}} {{1,2,3},{1,2,4},{1,3,4},{2,3,4}} MATHEMATICA stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]]; fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; Table[Length[fasmax[stableSets[Subsets[Range[n], {2, n}], Or[Intersection[#1, #2]=={}, SubsetQ[#1, #2]]&]]], {n, 0, 5}] (* 2nd program *) n = 2^6; g = CompleteGraph[n]; i = 0; While[i < n, i++; j = i; While[j < n, j++; If[BitAnd[i, j] == 0 || BitAnd[i, j] == i || BitAnd[i, j] == j, g = EdgeDelete[g, i <-> j]]]]; sets = FindClique[g, Infinity, All]; Length[sets]-Log[2, n]-1 (* Elijah Beregovsky, May 06 2020 *) CROSSREFS Antichains of nonempty, non-singleton sets are A307249. Minimal covering antichains are A046165. Maximal intersecting antichains are A007363. Maximal antichains of nonempty sets are A326359. Cf. A000372, A003182, A006126, A006602, A014466, A051185, A058891, A261005, A305000, A305844, A326358, A326360, A326361, A326363. Sequence in context: A309440 A226012 A011552 * A287222 A216598 A219397 Adjacent sequences: A326359 A326360 A326361 * A326363 A326364 A326365 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 01 2019 EXTENSIONS a(7) from Elijah Beregovsky, May 06 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 31 21:32 EDT 2023. Contains 363068 sequences. (Running on oeis4.)