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Counting Finite Lattices

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Abstract.

The correct values for the number of all unlabeled lattices on n elements are known for \( n \leq 11 \). We present a fast orderly algorithm generating all unlabeled lattices up to a given size n. Using this algorithm, we have computed the number of all unlabeled lattices as well as that of all labeled lattices on an n-element set for each \( n \leq 18 \).

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Authors and Affiliations

  1. Universität Hannover, Institut für Mathematik, Welfengarten 1, 30167 Hannover, Germany, e-mail: heitzig@math.uni-hannover.de, , , , , , DE

    Jobst Heitzig

  2. Universität Hannover, Institut für Mathematik, Welfengarten 1, 30167 Hannover, Germany, e-mail: reinhold@math.uni-hannover.de, , , , , , DE

    Jürgen Reinhold

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  1. Jobst Heitzig
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  2. Jürgen Reinhold
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Additional information

Received April 4, 2000; accepted in final form November 2, 2001.

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ID="h1" Presented by R. Freese.

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Heitzig, J., Reinhold, J. Counting Finite Lattices. Algebra univers. 48, 43–53 (2002). https://doi.org/10.1007/PL00013837

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  • DOI: https://doi.org/10.1007/PL00013837

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