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Periodicity of residues of the number of finite labeled To-topologies

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Abstract

Let T0(n) be the number of labeled topologies on points satisfying the To separation axiom. It is proved that for any prime p the sequence of residue classes To(n) mod p is periodic with period length p−1.

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Literature cited

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

  2. Z. I. Borevich, “Periodicity of the residues of the number of finite labeled topologies,” J. Sov. Math. (in preparation).

  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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Authors
  1. Z. I. Borevich
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 32–36, 1982.

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Borevich, Z.I. Periodicity of residues of the number of finite labeled To-topologies. J Math Sci 27, 2851–2854 (1984). https://doi.org/10.1007/BF01410738

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  • DOI: https://doi.org/10.1007/BF01410738

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