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A326358 Number of maximal antichains of subsets of {1..n}. 10
1, 2, 3, 7, 29, 376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A set system (set of sets) is an antichain if no element is a subset of any other.

LINKS

Table of n, a(n) for n=0..5.

FORMULA

For n > 0, a(n) = A326359(n) + 1.

EXAMPLE

The a(0) = 1 through a(3) = 7 maximal antichains:

  {}  {}   {}      {}

      {1}  {12}    {123}

           {1}{2}  {1}{23}

                   {2}{13}

                   {3}{12}

                   {1}{2}{3}

                   {12}{13}{23}

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]], SubsetQ]]], {n, 0, 5}]

CROSSREFS

Antichains of sets are A000372.

Minimal covering antichains are A046165.

Maximal intersecting antichains are A007363.

Maximal antichains of nonempty sets are A326359.

Cf. A003182, A006126, A006602, A014466, A058891, A261005, A305000, A305001, A305844, A326360, A326361, A326362, A326363.

Sequence in context: A072469 A004062 A037151 * A008840 A268477 A156313

Adjacent sequences:  A326355 A326356 A326357 * A326359 A326360 A326361

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 01 2019

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)