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Some recurrence relations in finite topologies

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Abstract

In a number of papers (see, e.g., RZhMat, 1977, 11B586) there is given for the number To(n) of labeled topologies on n points satisfying the To separation axiom the formula

$$T_0 (n) = \sum {\frac{{n!}}{{p_1 ! \ldots p_k !}}V(p_1 , \ldots p_k ),} $$

where the summation extends over all ordered sets (p1,...,Pk) of natural numbers such that p1+...+Pk=n. In the present paper there is found a relation for calculating, whenn⩾2, the sum of all terms in this formula for which p2=1 in terms of the values V(q1,...,qt) withq1+...+qt⩽n-2. This permits the determination (with the aid of a computer) of the new value To(12)=414 864 951 055 853 499

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Literature cited

  1. Z. I. Borevich, “On the enumeration of finite topologies,” J. Sov. Math.,20, No. 6 (1982).

  2. V. I. Rodionov, “A relation in finite topologies,”J. Sov. Math.,24, No. 4 (1984).

  3. L. Comtet, “Recouvrements, bases de filtre et topologies d'un ensemble fini,” C. R. Acad. sci.,AB262, No. 20, A1091-A1094 (1966).

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  4. S. K. Das, “A machine representation of finite To topologies,” J. Asso. Comput. Mach.,24, No. 4, 676–692 (1977).

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  5. M. Erné, “On the cardinalities of finite topologies and the number of antichains in partially ordered sets,” Discrete Math.,35, 119–133 (1981).

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Authors
  1. V. I. Rodionov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 174–179, 1982.

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Rodionov, V.I. Some recurrence relations in finite topologies. J Math Sci 27, 2963–2968 (1984). https://doi.org/10.1007/BF01410750

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  • DOI: https://doi.org/10.1007/BF01410750

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