A326358 - OEIS

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A326358

Number of maximal antichains of subsets of {1..n}.

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	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`

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