A334252 Number of closure operators on a set of n elements which satisfy the T_0 separation axiom.
1, 2, 5, 44, 2179, 1362585, 75953166947, 14087646640499308474
Offset: 0
Examples
The a(0) = 1 through a(2) = 5 set-systems of closed sets: {{}} {{}} {{1,2},{1}} {{1},{}} {{1,2},{2}} {{1,2},{1},{}} {{1,2},{2},{}} {{1,2},{1},{2},{}}
Links
- R. S. R. Myers, J. Adámek, S. Milius, and H. Urbat, Coalgebraic constructions of canonical nondeterministic automata, Theoretical Computer Science, 604 (2015), 81-101.
- B. Venkateswarlu and U. M. Swamy, T_0-Closure Operators and Pre-Orders, Lobachevskii Journal of Mathematics, 39 (2018), 1446-1452.
Crossrefs
Formula
a(n) = Sum_{k=0..n} Stirling1(n,k) * A102896(k). - Andrew Howroyd, Apr 20 2020
Extensions
a(6)-a(7) from Andrew Howroyd, Apr 20 2020
Comments