login
A355517
Number of nonisomorphic systems enumerated by A334254; that is, the number of inequivalent closure operators on a set of n elements where all singletons are closed.
1
1, 2, 1, 4, 50, 7443, 95239971
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
a(0) = 1 counts the empty set, while a(1) = 2 counts {{1}} and {{},{1}}.
For a(2) = 1 the closure system is as follows: {{1,2},{1},{2},{}}.
The a(3) = 4 inequivalent set-systems of closed sets are:
{{1,2,3},{1},{2},{3},{}}
{{1,2,3},{1,2},{1},{2},{3},{}}
{{1,2,3},{1,2},{1,3},{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, while A193674 contains the number of all nonisomorphic ones.
For T_1 closure operators and their strict counterparts, see A334254 and A334255, respectively; the only difference is a(1).
Sequence in context: A061655 A009830 A053374 * A227050 A093876 A375605
KEYWORD
nonn,hard,more
AUTHOR
Dmitry I. Ignatov, Jul 05 2022
STATUS
approved