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A334254
Number of closure operators on a set of n elements which satisfy the T_1 separation axiom.
5
1, 2, 1, 8, 545, 702525, 66960965307
OFFSET
0,2
COMMENTS
The T_1 axiom states that all singleton sets {x} are closed.
For n>1, this property implies strictness (meaning that the empty set is closed).
EXAMPLE
The a(3) = 8 set-systems of closed sets:
{{1,2,3},{1},{2},{3},{}}
{{1,2,3},{1,2},{1},{2},{3},{}}
{{1,2,3},{1,3},{1},{2},{3},{}}
{{1,2,3},{2,3},{1},{2},{3},{}}
{{1,2,3},{1,2},{1,3},{1},{2},{3},{}}
{{1,2,3},{1,2},{2,3},{1},{2},{3},{}}
{{1,2,3},{1,3},{2,3},{1},{2},{3},{}}
{{1,2,3},{1,2},{1,3},{2,3},{1},{2},{3},{}}
CROSSREFS
The number of all closure operators is given in A102896.
For T_0 closure operators, see A334252.
For strict T_1 closure operators, see A334255, the only difference is a(1).
Sequence in context: A013327 A359625 A009349 * A230582 A011186 A078088
KEYWORD
nonn,more,hard
AUTHOR
Joshua Moerman, Apr 20 2020
EXTENSIONS
a(6) from Dmitry I. Ignatov, Jul 03 2022
STATUS
approved