0,2

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}}. The T_0 condition means that the dual is strict (no repeated edges).

Non-isomorphic representatives of the a(1) = 2 through a(4) = 23 set-systems:

0 0 0 0

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

{1}{12} {1}{12} {1}{12}

{1}{12}{13} {1}{12}{13}

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

{1}{12}{13}{123} {1}{12}{13}{14}

{1}{12}{13}{123}

{1}{12}{13}{124}

{1}{12}{123}{124}

{1}{12}{13}{1234}

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

{1}{12}{13}{14}{123}

{1}{12}{13}{123}{124}

{1}{12}{13}{14}{1234}

{1}{12}{13}{123}{1234}

{1}{12}{13}{124}{1234}

{1}{12}{123}{124}{1234}

{1}{12}{13}{14}{123}{124}

{1}{12}{13}{14}{123}{1234}

{1}{12}{13}{123}{124}{1234}

{1}{12}{13}{14}{123}{124}{134}

{1}{12}{13}{14}{123}{124}{1234}

{1}{12}{13}{14}{123}{124}{134}{1234}

The labeled version is A326959.

T_0 set-systems are A326940.

Cf. A051185, A059201, A319559, A309615, A319637, A326944, A326945, A326946.

Sequence in context: A317973 A393786 A361333 * A171708 A329565 A295967

Adjacent sequences: A327010 A327011 A327012 * A327014 A327015 A327016

nonn,more

Gus Wiseman, Dec 10 2019

a(5)-a(6) from Andrew Howroyd, Dec 21 2019

approved