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, Volume 8, Issue 3, pp 247–265 | Cite as

Counting finite posets and topologies

  • Marcel Erné
  • Kurt Stege
Article

Abstract

A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. Using these numbers in connection with certain formulae derived earlier by the first author, one can now compute the numbers of all quasiordered sets, posets, connected posets etc. with n points for n≤14. Using the well-known one-to-one correspondence between finite quasiordered sets and finite topological spaces, one obtains the numbers of finite topological spaces with n points and k open sets for n≤11 and all k, and then the numbers of all topologies on n≤14 points satisfying various degrees of separation and connectedness properties, respectively. The number of (connected) topologies on 14 points exceeds 1023.

AMS subject classifications (1991)

05A15 05A19 06A06 54-04 

Key words

Quasiordered set partially ordered set topology connected separation axiom antichain generating function 

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Marcel Erné
    • 1
  • Kurt Stege
    • 1
  1. 1.Institut für MathematikUniversität HannoverHannoverGermany

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