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 A334252 Number of closure operators on a set of n elements which satisfy the T_0 separation axiom. 2
 1, 2, 5, 44, 2179, 1362585, 75953166947, 14087646640499308474 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The T_0 axiom states that the closure of {x} and {y} are different for distinct x and y. LINKS Table of n, a(n) for n=0..7. 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. FORMULA a(n) = Sum_{k=0..n} Stirling1(n,k) * A102896(k). - Andrew Howroyd, Apr 20 2020 EXAMPLE 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},{}} CROSSREFS The number of all closure operators is given in A102896. For strict T0 closure operators, see A334253. For T1 closure operators, see A334254. Cf. A326943, A326944, A326945. Sequence in context: A163115 A221682 A088309 * A307147 A056680 A005166 Adjacent sequences: A334249 A334250 A334251 * A334253 A334254 A334255 KEYWORD nonn,more AUTHOR Joshua Moerman, Apr 20 2020 EXTENSIONS a(6)-a(7) from Andrew Howroyd, Apr 20 2020 STATUS approved

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Last modified September 29 02:18 EDT 2023. Contains 365748 sequences. (Running on oeis4.)