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A326360 Number of maximal antichains of nonempty, non-singleton subsets of {1..n}. 7
1, 1, 1, 2, 13, 279, 29820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.

EXAMPLE

The a(1) = 1 through a(4) = 13 maximal antichains:

  {}  {12}  {123}         {1234}

            {12}{13}{23}  {12}{134}{234}

                          {13}{124}{234}

                          {14}{123}{234}

                          {23}{124}{134}

                          {24}{123}{134}

                          {34}{123}{124}

                          {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], {2, n}], SubsetQ]]], {n, 0, 4}]

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, A058891, A261005, A305000, A305844, A326358, A326361, A326362, A326363.

Sequence in context: A042677 A134296 A086510 * A123113 A126742 A013051

Adjacent sequences:  A326357 A326358 A326359 * A326361 A326362 A326363

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 December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)