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A326972 Number of unlabeled set-systems on n vertices whose dual is a (strict) antichain, also called unlabeled T_1 set-systems. 15
1, 2, 4, 20, 1232 (list; graph; refs; listen; history; text; internal format)



A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of sets, none of which is a subset of any other.


Table of n, a(n) for n=0..4.


Non-isomorphic representatives of the a(0) = 1 through a(3) = 20 set-systems:

{} {} {} {}

{{1}} {{1}} {{1}}

{{1},{2}} {{1},{2}}

{{1},{2},{1,2}} {{1},{2},{3}}


















Unlabeled set-systems are A000612.

Unlabeled set-systems whose dual is strict are A326946.

The version with empty edges allowed is A326951.

The labeled version is A326965.

The version where the dual is not required to be strict is A326971.

The covering version is A326974 (first differences).

Cf. A059523, A319559, A319637, A326973, A326976, A326977, A326979.

Sequence in context: A325050 A325503 A087314 * A099179 A102049 A058522

Adjacent sequences: A326969 A326970 A326971 * A326973 A326974 A326975




Gus Wiseman, Aug 11 2019



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Last modified November 27 14:32 EST 2022. Contains 358405 sequences. (Running on oeis4.)