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A326359 Number of maximal antichains of nonempty subsets of {1..n}. 9
1, 1, 2, 6, 28, 375, 31745 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..6.

FORMULA

For n > 0, a(n) = A326358(n) - 1.

EXAMPLE

The a(0) = 1 through a(4) = 28 antichains:

  {}   {1}    {12}      {123}           {1234}

              {1}{2}    {1}{23}         {1}{234}

                        {2}{13}         {2}{134}

                        {3}{12}         {3}{124}

                        {1}{2}{3}       {4}{123}

                        {12}{13}{23}    {1}{2}{34}

                                        {1}{3}{24}

                                        {1}{4}{23}

                                        {2}{3}{14}

                                        {2}{4}{13}

                                        {3}{4}{12}

                                        {1}{2}{3}{4}

                                        {12}{134}{234}

                                        {13}{124}{234}

                                        {14}{123}{234}

                                        {23}{124}{134}

                                        {24}{123}{134}

                                        {34}{123}{124}

                                        {1}{23}{24}{34}

                                        {2}{13}{14}{34}

                                        {3}{12}{14}{24}

                                        {4}{12}{13}{23}

                                        {12}{13}{14}{234}

                                        {12}{23}{24}{134}

                                        {13}{23}{34}{124}

                                        {14}{24}{34}{123}

                                        {123}{124}{134}{234}

                                        {12}{13}{14}{23}{24}{34}

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

CROSSREFS

Antichains of nonempty sets are A014466.

Minimal covering antichains are A046165.

Maximal intersecting antichains are A007363.

Maximal antichains of sets are A326358.

Cf. A000372, A003182, A006126, A006602, A014466, A058891, A261005, A305000, A305844, A307249, A326360, A326362, A326363.

Sequence in context: A108800 A325507 A306793 * A136639 A284594 A027109

Adjacent sequences:  A326356 A326357 A326358 * A326360 A326361 A326362

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 01 2019

EXTENSIONS

a(6) from Andrew Howroyd, Aug 14 2019

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)